SCH BASIC A APPI SCIC Science.… · 4 3.1 B. Sc. (Hons.) Chemistry This course aims to impart...

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B.Sc. (Hons.) ChemistryB.Sc. (Hons.) Physics

B.Sc. (Hons.) Mathematics2019-20

SCHOOL OF BASICAND

APPLIED SCIENCE

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Content

1. Introduction 3

2. About School 3

3. Programmes offered by the School 3

3.1 B.Sc. (Hons.) Chemistry 4

3.2 B.Sc. (Hons.) Physics 4

3.3 B.Sc. (Hons.) Mathematics 4

4. Programme Duration 5

5. Class Timings 5

6. Syllabi 5

6.1 Syllabus of Common Courses in all B.Sc. (Hons.) Programme 5-8

6.2 Syllabus of Common Courses in B.Sc. (Hons.) Chemistry and Mathematics 9-11

6.3 Syllabus of Common Courses in B.Sc. (Hons.) Physics and Mathematics 11-12

6.4 Syllabus of Courses specific to B.Sc. (Hons.) Chemistry 12-16

6.5 Syllabus of Courses specific to B.Sc. (Hons.) Physics 16-18

6.6 Syllabus of Courses specific to B.Sc. (Hons.) Mathematics 18-27

7. Annexures

7.1 Annexure-A 28-29

7.2 Annexure-B 30-32

7.3 Annexure-C 33

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1. IntroductionThe K.R. Mangalam Group has made a name for itself in the field of education. Over a period of time, the various educational entities of the group have converged into a fully functional corporate academy. Resources at KRM have been continuously upgraded to optimize opportunities for the students. Our students are groomed in a truly inter-disciplinary environment wherein they develop integrative skills through interaction with students from engineering, management, journalism and media study streams.

The K.R. Mangalam story goes back to the chain of schools that offered an alternative option of world-class education, pitching itself against the established elite schools, which had enjoyed a position of monopoly till then. Having blazed a new trail in school education, the focus of the group was aimed at higher education. With the mushrooming of institutions of Higher Education in the National Capital Region, the university considered it very important that students take informed decisions and pursue career objectives in an institution, where the concept of education has evolved as a natural process.

K.R. Mangalam University was founded in the year 2013 by Mangalam Edu Gate, a company incorporated under Section 25 of the Companies Act, 1956.

K. R. Mangalam University is unique because of itsi. Enduring legacy of providing education to high achievers who demonstrate leadership

in diverse fields.ii. Protective and nurturing environment for teaching, research, creativity, scholarship,

social and economic justice.

Objectivesi. To impart undergraduate, post-graduate and Doctoral education in identified areas of

higher education.ii. To undertake research programmes with industrial interface.iii. To integrate its growth with the global needs and expectations of the major stake holders

through teaching, research, exchange & collaborative programmes with foreign, Indian Universities/Institutions and MNCs.

iv. To act as a nodal center for transfer of technology to the industry.v. To provide job oriented professional education to the pecia student community with

particular focus on Haryana.

2. About SchoolThe school imparts out both teaching and research through its various science disciplines viz Mathematics, Chemistry and Physics.

School of Basic and Applied Sciences imparts students technical knowledge, enhances their skill and ability, motivating them to think creatively, helping them to act independently and take decisions accordingly in all their scientific pursuits and other endeavors. It strives to empower its students and faculty members to contribute to the development of society and Nation.

The faculty is in constant touch with various experts in the relevant field and is willing to experiment with latest ideas in teaching and research.

The School comprises of Discipline of Chemistry, Physics and Mathematics.

3. Programmes offered by the SchoolSchool offers undergraduate B.Sc. (Hons) Programmes and postgraduate M.Sc. Programmes. All these programmes are designed to impart scientific knowledge to the students and will provide theoretical as well as practical training in their respective fields.

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3.1 B. Sc. (Hons.) ChemistryThis course aims to impart basic and applied knowledge in various branches in Chemistry with a view to produce good academics, researchers and professionals in the field.

Eligibility Criteria:- The student should have passed the 10+2 examination conducted by the Central Board of Secondary Education or equivalent examination from a recognized Board in Science stream with an aggregate of 50% or more.

Course Outline:- Inorganic chemistry / Organic chemistry / Physical chemistry / Analytical methods in chemical sciences / Environmental chemistry / Biochemistry / Green Chemistry.

Career Options:- Opportunities exist in chemical industry, pharmacy, education and forensics.

Programme scheme: - For Programme scheme see Annexure A.

3.2 B.Sc. (Hons.) PhysicsPhysics, as a stream of study, helps in understanding fundamentals and develop curiosity in understanding various physical aspects of universe. This course aims to impart basic and applied knowledge in physics with a view to produce good academicians, researchers and professionals in varied fields.

Eligibility Criteria: - The student should have passed the 10+2 examination conducted by the Central Board of Secondary Education or equivalent examination from a recognized Board in Science stream with an aggregate of 50% or more.

Course Outline: - Mathematical Physics / Mechanics / Electricity & Magnetism/Waves & Optics / Thermal Physics / Digital Systems & Applications/Elements of Modern Physics/Analog Systems & Applications/Quantum Mechanics & Applications / Electromagnetic Theory / Statistical Mechanics/Solid State physics / Elementary Nuclear Physics/ Elementary Particle Physics/Applied Optics.

Career Options: - Opportunities exist in academics, research laboratories and administration besides all the opportunities applicable to any other graduate like UPSC examination’s, defence services and other govt. jobs.

Programme scheme: - For Programme scheme see Annexure B.

3.3 B.Sc. (Hons.) MathematicsMathematics is a universal part of human culture. This course aims to impart basic and applied knowledge in Mathematics with a view to produce good Mathematicians and researchers. A degree in mathematics provides you with a broad range of skills in problem solving, logical reasoning and flexible thinking.

Eligibility Criteria: - The student should have passed the 10+2 examination conducted by the Central Board of Secondary Education or equivalent examination from a recognized Board with an aggregate of 50% or more with Mathematics as a main subject.

Course Outline: - Calculus / Vector Calculus / Business Mathematics / Differential Equations / Solid Geometry / Computer Programming / Modern Algebra / Numerical Analysis / Linear Algebra / Real Analysis / Complex Analysis / Probability and Statistics / Operational research / Mechanics.

Career Options: - Mathematicians work in business, finance, industry, government offices, management, education and science.

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Programme scheme: - For Programme scheme see Annexure C.

4. Programme DurationThe minimum period required for the B.Sc. (Hons.) Programme offered by the University shall extend over a period of three Academic Years.

The maximum period for the completion of the B.Sc. (Hons) Programme offered by the University shall be five years.

5. Class TimingsThe classes will held from Monday to Friday from 09:10 am to 04:10 pm.

6. SyllabiThe syllabi of all courses for first year for all the programmes offered by SBAS are given in the following pages. These are arranged as: (a) common courses (b) degree specific courses, in numeric order of the last three digits of the course code.

For each course, the first line contains; Course Code and Credits (C) of the course. This is followed by the course objectives, syllabus (Unit I to IV), Text book and reference books.

6.1 Syllabi of Common Courses in all B.Sc. (Hons.) Programme

BSCH125A ENVIRONMENTAL STUDIES (Credits 3)

Overview:Everything that surrounds and affects living organisms is environment. Environment includes all those things on which we are directly or indirectly dependent for our survival, whether it is living or biotic components like animals, plants or non-living or abiotic components like soil, air and water etc. It belongs to all, influences all and is important to all.

Environmental Protection Act (1986) defined “Environment as the sum total of water, air and land, their interrelationship among themselves and with the human beings, other living organisms and materials.” Environmental studies are important since it deals with the most mundane problems of life like hygienic living conditions, safe and clean drinking water, fresh air, healthy food and sustainable development.

The syllabus for Environmental Studies includes conventional class room teaching as well as field work. In this course the teacher simply acts as a catalyst to infer what the student observes or discovers in his/her own environment. Involvement of students in project work is one of the most effective learning tools for environmental issues. This syllabus is beyond the scope of text book teaching and also the realm of real learning by observing the surroundings. The content of this course provides an overview of introduction to environment, concept of an ecosystem, various renewable and non-renewable resources, how are various biodiversity occur and different means to conserve these. This course also includes various types of pollution and environmental policies & practices related with environs. Finally, it also highlights the relationship of human population with environment. The course further integrates to project work such as visit to an area to document environmental assets river/ forest/ grassland/ hill/ mountain, visit to a local polluted site-Urban/Rural/Industrial/Agricultural, study of common plants, insects, birds, and study of simple ecosystems. These studies are as imperative as it forms a unique synergistic tool for comprehensive learning process. This will help students to recognize and appreciate how the technological advancement at global level, exponential growth of human population and their unlimited demands has put the environment at stake and has contaminated the environment worldwide.

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Objective and Expected Outcome:The main objective of the course is to create consciousness among the students with the idea about healthy and safe environment. This course is aimed to explain students that the rapid industrialization, crazy consumerism and over-exploitation of natural resources have resulted in degradation of earth at all levels. These changes need the discussion, concern and recognition at national and international level with respect to formulate protection acts and sustainable developments policies. It can be possible only if every citizen of the nation is environmentally educated and gets involved into this matter at the grass root level to mitigate pollution.

After studying the course, the learners will be able to comprehend and become responsive regarding environmental issues. They will acquire the techniques to protect our mother earth, as without a clean, healthy, aesthetically beautiful, safe and secure environment no specie can survive and sustain. This is the only inheritance which every genera of specie passes to their future generation.

BSCS102A INFORMATION TECHNOLOGY FUNDAMENTALS (Credits 4)

Overview:Computing and programming is essential to leverage the technical skills of a student. These techniques equip the students with know-how of the latest technologies and reduce considerable time in solving problems. Success in college and beyond requires computer and information literacy’s that are flexible enough to change with a changing IT environment and adaptable to new problems and tasks. The purpose of the information technology requirement is to ensure that students achieve an essential understanding of information technology infrastructure encompassing systems and devices; and become more sophisticated technology users and consumers.

Objectives and Expected Outcome: The main objective is to introduce IT in a simple language to all undergraduate students, regardless of their specialization. It will help them to pursue specialized programs leading to technical and professional careers and certifications in the IT industry. The focus of the subject is on introducing skills relating to IT basics, computer applications, programming, interactive media, Internet basics, etc.

The aims is to: 1. Understand basic functions of computer software components including operating system functions; 2. Develop a critical attitude to gathering, processing and evaluating information; 3. Develop a broad understanding of hardware, software, networks, databases and information systems and their uses; 4. Sensitise students to the use of Information Technology in conducting and living their daily lives; 5. Develop an awareness of the power and pitfalls of Information Technology.

OPEN ELECTIVE COURSE I:

IIIT101A HARNESSING THE POWER OF THE WEB AS A KNOWLEDGE DEVICE (Credits 4)

Overview:This course will give the learner an understanding of internet as a medium of learning. "Internet" is a gigantic library where information about almost any subject is available in depth and up to date. Through this program the student learns to appreciate the richness of the Web and the Internet, and gets an understanding to make clear what is reality and what is false propaganda and uses his/her own intelligence or mind to investigate further.

Internet has been incredibly useful as a learning medium as it facilitates both information and communication. The Internet has increased the accessibility of education at all levels and has

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turned out to be a giant repository of knowledge as it is not only a great place to gather and store information but also allows its easy retrieval whenever desired. In fact, it has turned out to be better than libraries when it comes to gathering information and doing research work.

The Internet expeditiously entered the life of the humankind in the 20th century. Less than a decade back we did not know much about the modern Internet and imagine its facilities and our life with it. In few years now it has become not only the hugest information resource in the world. Internet provides unique learning opportunities as the very idea behind invention of internet was education.

Today we live in an information society where knowledge has great value and knowledge can be manifested through qualification. All the countries are using high-end technology which needs highly qualified specialists. Web can be a very effective in promoting this process.

The most important thing is the ability to work with information because it demands a student’s ability to use different kinds of intellectual skills. It means that a student should be able to analyze the information he deals with, to select the facts, data adequate to the problem he investigates.

The information the student comes across in the Internet is not always helpful. The Internet is a very democratic environment where every user can locate his/her information. A lot of educational materials do not undergo any examination. Besides, we should keep in mind that reading electronic texts in the net is not like reading printed texts.

For effective education a mere access to Internet information resources is not enough. It is necessary to prepare the students beforehand to work with information. The goal of this program is to develop critical thinking of student so that he or she can use internet for effective learning.

Objective and Expected Outcome:The usage of the information resources located in the Internet is not such a simple affair. It requires not only the ability to search for it in the huge ocean of the Internet, but to process it, to use it effectively for the cognitive goals. Through this course the student will develop skills to use search engines effectively for learning and research.

The growth of the Internet has provided many opportunities people in different ways. Students consider the use of the Internet is mainly for information, social and entertainment purposes but the Internet provides huge academic and scientific information as well which makes it as a tool to learn. It provides asynchronous education to student, as they are passionate internet lovers and prefer to use web for information.

The course equips the student to find information on web and use critically and creatively, to become collaborative and cooperative workers and to solve problems

BSEL101A COMMUNICATION SKILLS (Credits 5)

Overview:The world is shrinking into a global village and therefore, communication skills in English have emerged as a major means of empowerment and human resource development. Many professionals fail to make an impact on the global market as they lack the required communicative competence. The course with its practice-based learning tasks will facilitate the learners to enhance their communication skills in a modern and globalized context. It will enhance the linguistic and communicative competence of the learners and hone their interpersonal skills. This course will augment comprehension skills, enhance vocabulary, acquire impressive writing skills, correspond with others effectively, understand the non-verbal cues and enhance skills in spoken English through a variety of teaching techniques. The course will be instrumental in acquiring proficiency both in spoken and oral language.

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Objective and Expected Outcome:The course will help the learners to focus on communication activities in functional and situational contexts as well as enhance the four language skills of reading, writing, listening and speaking through real-life and professional situations. It will build confidence among the students and encourage them to speak fluently. Through practical learning and delivery, the learners will be able to identify their areas of strengths and weaknesses and improvise their personality and soft skills. The learners will be able to strengthen and broaden their communication skills through various insightful ways.

OPEN ELECTIVE COURSE II:

IIIT104A UNDERSTANDING THE POWER OF DATA (Credits-4)

Overview:This course is designed to provide students with hands-on experience for gaining an understanding of numbers and data for building models.

Why data is so important in our life? Many of us are knowingly or unknowingly using it but are unknown about the fact. Such as “I sleep for about 8 hours a day.”, “I usually drive at 50 km/hr.”, “If I start early then the chances that I will pass in the exam are higher.” or “Which political party will win next assembly elections?” These are nothing but statistical in nature. We are constantly gathering, organizing and analyzing information, and using it to make judgments and decisions that affect our actions.

This course aims to enable students to figure out and solve problems on their own and use technology efficiently. The activities are designed to encourage students to take accountability for their own learning. The skills the students acquire during the course are necessary for the needs and challenges of the country.

Objective and Expected Outcome:This course encourages students to blend theoretical and practical knowledge, and transfer it into practice. The themes on which the course is based are –

• Interesting properties of prime numbers without proofs • Analysis of data for simple quantitative inference• Correlate real-world observations with theoretical knowledge• Compute and validate probabilities • Use of spreadsheets and R for practical work• Statistical analysis of the stock market, weather, and daily life data.

Data can be used to describe situations or events. For instance, a manufacturer might want to know something about the consumers who will be purchasing his product so he can plan an effective marketing strategy. In another situation, a buyer might survey before purchasing a product. For example, when we purchase a cell phone we look at various features and specifications provided by different companies. Further, trends in the market can be analyzed, enabling prospective buyers to make more intelligent decisions. These examples illustrate a few situations where collecting and analyzing data will help students make better decisions.

The course is about exercising the brain and learning new ideas, not to just mimic steps, procedures, and formulas. The students are expected to acquire the ability to overcome obstacles and keep trying until they reach a goal.

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6.2 Syllabi of Common Courses in B.Sc. (Hons.) Chemistry and Mathematics


BSPH120A CONDENSED MATTER PHYSICS (Credits 4)

Overview:Physics and chemistry may overlap when the system under study involves matter composed of electrons and nuclei made of protons and neutrons. On the other hand, chemistry is not concerned with other forms of matter such as quarks, mu and tau leptons and dark matter. Although fundamental laws that govern the behavior of matter apply both in chemistry and physics, the disciplines of physics and chemistry are distinct.

Physics is concerned with nature from a very large scale (the entire universe) down to a very small scale (subatomic particles). All physical phenomena that are measurable follow some behavior that is in accordance with the most basic principles studied in physics.

Physics is involved with the fundamental principles of physical phenomena and the basic forces of nature, and also gives insight into the aspects of space and time. The course deals with the basic principles that explain matter and energy, and may study aspects of atomic matter by following concepts derived from the most fundamental principles viz spectroscopy, thermodynamics, solid state physics, and crystallography.

Objective and Expected Outcome:Spectroscopy is used in physical and analytical chemistry because atoms and molecules have unique spectra. The measured spectra are used to determine the chemical composition and physical properties of astronomical objects (such as their temperature and velocity).

The main objectives of the concept of studying thermodynamics to determine the feasibility of the reaction.

This course gives an introduction to solid state physics, and will enable the student to employ classical and quantum mechanical theories needed to understand the physical properties of solids. Emphasis is put on building models which will be able to explain several different phenomena in the solid state.

Crystallography explains the salient points of higher-symmetry space groups, namely those belonging to the tetragonal, trigonal, hexagonal, and cubic crystal systems through mathematical concepts.

After the end of this course, the student will be able to:

• Interpret UV-Visible spectroscopy, explain basic principles of UV-Visible spectroscopy, will be able to interpret IR spectroscopy, explain basic principles of IR spectroscopy, explain working principles and taking spectrum of IR spectroscopy device, will be able to interpret NMR spectroscopy, explain basic principles of NMR spectroscopy, explain sample preparation procedure in NMR spectroscopy and will be able to interpret elemental analysis technique.

• Explain the concepts of entropy, enthalpy and Ideal gas equation and various gas Laws: Student should able to understand Entropy and its application. Student should able to understand Gas Laws. Student should able to understand thermodynamic processes. Entropy understands the role of thermodynamic cycles, availability and irreversibility. Student should able to quantify the behavior Gas Power Cycles cycle. Student should able to understand concept of Availability. Student should able to understand concept of irreversibility and second law efficiency.

• Explains the fundamental concepts of solid state physics such as what types of matter exist and the methods available to determine their structure and properties. Outline

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the physical origins which govern the properties of matter in the solid state. Apply the knowledge gained to solve problems in solid state physics using relevant mathematical tools.


BSPH217A APPLICATIONS OF MATERIALS (Credits-4)

Overview:Both physics and chemistry are concerned with matter and its interaction with energy, the two disciplines differs in approach. In physics, it is typical to abstract from the specific type of matter, and to focus on the common properties of many different materials. In optics, for example, materials are characterized by their index of refraction, and materials with the same index of refraction will have identical properties. Chemistry, on the other hand, focuses on what compounds are present in a sample, and explores how changing the structure of molecules will change their reactivity and their physical properties. Chemistry and physics are interrelated, chemists and physicists work in teams to explore the following topics in this current course related with Material Science, Nuclear physics, and Nanomaterials.

Objective and Expected Outcome:The use of fundamental sciences and their principles relevant to materials that include the relationships between nano/microstructure, characterization, properties, processing, performance and design of materials. The study of nuclear physics is the understanding of the "Structure of Nuclei". A most basic property of a nucleus is its binding energy. This is brought about by the specific nuclear forces, counteracted partially by the Coulomb repulsion between the protons. An understanding of the structure-property relationships in nano-materials as well as the concepts, not applicable at larger length scales, that need to be taken into consideration for nano-science and nanotechnology. To make quantitative predictions about whether, equilibrium will favour products or reactants in a redox reaction. Imagine each of the above as a competition to gain electrons.

After completion of the course the student should be able to:

• Describe the basic structure of materials at the molecular, microscopic, and macroscopic scales, and will be able to describe modern methods of characterizing materials at each of these length scales. Students will understand diffusion and electrochemical processes in materials.

• Explain the ground state properties of the nucleus for study of the nuclear structure behavior. They can explain the deuteron behavior at ground and excited states. They can apply deuteron physics and the Nucleon-Nucleon scattering for explaining the nuclear forces. They can able to demonstration of the shell model and collective model descriptions. They can apply various aspects of nuclear reactions in view of compound nuclear dynamics.

• Qualitatively describe how the nanoparticle size can affect the morphology, crystal structure, reactivity, and electrical properties.

• Describe several synthesis methods for fabrication of inorganic nanoparticles, one-dimensional nanostructures (nanotubes, nanorods, nanowires), thin films, nanoporous materials, and nanostructured bulk materials, and also could describe how different lithography methods can be used for making nanostructures. The student should have a theoretical background within synthesis/fabrication of nanomaterials which makes he/she prepared for later literature studies and laboratory work within the field.

• Perform simple geometric calculations of surface energy, coordination number, and volume fraction related to nanoscale properties and synthesis, and also simple chemical calculations related to synthesis.

• Use the acquired knowledge to evaluate which synthesis methods that can be best

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suited for fabricating nanostructured materials of various inorganic compounds (metals, semiconductors, oxides, fullerenes) and constructions of these.

6.3 Syllabi of Common Courses in B.Sc. (Hons.) Physics and Mathematics


BSCH110A FUNDAMENTALS OF CHEMISTRY & WATER PROCESSES (Credits 4)

Overview:This course inculcates the thought process of basic understanding of chemistry for the students of Mathematics and Physics background. It is a mandatory requirement to include chemistry in their course curriculum, which would helpful in their future education. All the higher education and professional context depends on basic sciences, which can relate the theories or concepts based on chemistry. Our daily life processes have an intense relation with chemistry. So, there is a need of an hour to provide exposure of basic chemistry to the students.

Objective and Expected Outcome:This course will enable the students to appreciate the developments in the field of chemical bonding with respect to Valence Bond theory and Molecular orbital theory. Students can relate these theories with structure and shapes of various homonuclear and heteronuclear molecules. This syllabus is mixture of all types of chemistry. In this course the students can understand basic concepts involved in organic reactions and appreciate the concept of geometric and optical isomerism. Water technology is a part of this course, which provides the complete processes of water quality analysis, hardness determination, softening and disinfection of water.

The outcome of this course enables the students for the analysis of the structure, composition of organic compounds, their orientation and optical activity of compounds. After studying this course students are also capable to determine water quality.


BSCH207A TECHNICAL INTERFACE OF CHEMISTRY (Credits 4)

Overview:This course inculcates the thought process of basic understanding of chemistry for the students of Mathematics and Physics background. It is a mandatory requirement to include chemistry in their course curriculum, which would helpful in their future prospects. All the higher education and professional context depends on basic sciences with respect to technical aspects, which can relate the theories or concepts based on chemistry. Our daily life processes have an intense relation with chemistry. So, there is a need of an hour to provide exposure of basic chemistry with some technical knowledge to the students.

Objective and Expected Outcome:This course will enable the students introduce basics of inorganic chemistry like periodic classification of elements and periodic properties, thermo chemistry and their application in engineering science and gain in site of phase and polymers. This syllabus is mixture of all types of chemistry. In this course the students can understand basic concepts involved in element classification and properties, variety of natural and synthetic fuels with respect to classification, analysis, carbonization, fractional distillation, thermal & catalytic cracking, octane &cetane No, and its significance; Power alcohol, Analysis of flue gases. The also enable to understand thermochemistry, phase rule (one component and two components) and polymer chemistry. The outcome of this course provides idea of different spheres of chemistry in one syllabus, which

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enables the student to understand periodic table, variety of fuels, thermochemistry and polymers.

6.4 Syllabi of Courses specific to B.Sc. (Hons.)Chemistry

OPEN ELECTIVE COURSE- I

BSMA141A FUNDAMENTALS OF CALCULUS (Credits 4)

Overview:Differential calculus and integral calculus are the basics for development of one of the main branch of mathematics, i.e. analysis, which has its application in other branches of science. In this course students will acquire knowledge regarding differential equation and numerical analysis and understand the field of matrix differential calculus and intergral calculus. This course will introduce students to numerical methods for solving ordinary differential equations

Objective and Expected Outcome:The objective of the course is to introduce students to the main topics of differential calculus namely, limits, continuity, and differentiation and their applications in tracing of curves, series expansion of algebraic, trigonometric, logarithmic functions etc. Finding roots using Graphical method, Bisection method and False position method. They will learn to solve a fixed point iteration method to obtain true roots, evaluate the True roots using Open method: Newton’s Rapson method, secant method and multiple Newton Rapson method, understand the pitfalls of Gauss Elimination Method. The goal is to provide a basic understanding of the derivation, analysis, and use of these numerical methods, along with a rudimentary understanding of finite precision arithmetic and the conditioning and stability of the various problems and methods. This will help students to choose, develop and apply the appropriate numerical techniques for the problem, interpret the results, and assess accuracy. Training in this course will not only open way to enter the branch of analysis in mathematics but also help students to handle problems in different branches of science i.e. physics, computer science, statistics, etc.

OPEN ELECTIVE COURSE- II

BSMA142A ESSENTIALS OF MATHEMATICS (Credits-4)

Overview:The course deals with fundamental concepts of differential equations, and the interrelationship between differential equations and linear algebra and the concept of existence and uniqueness of solutions of a differential equation, concept of a general solution, a particular solution and initial conditions, solve first order differential equation (both nonlinear and linear) using various techniques: integrating factor, separable differential equation, substitution method, exact differential equation and describes the basic notions of linear algebra such as vector, matrix, determinant, and eigenvalue.

Objective and Expected Outcome:The objectives of this course are to introduce students with both exact and numerical procedures for finding solutions to problems of differential equations. They will be given exposure to problems related to linear algebra. The course highlights the applications of linear algebra, complex logical arguments.

The primary learning outcome for this course is Quantitative Reasoning, which is to understand and apply mathematical concepts and reasoning, and analyze and interpret various types of data.

After the completion of the course, students will become competent in solving linear equations,

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performing matrix algebra, calculating determinants, and finding eigenvalues and eigenvectors. Students will be able to understand a matrix as linear transformations and they will differentiate between complex number and real number.

BSCH111A ATOMIC STRUCTURE AND CHEMICAL BONDING (Credits 5)Overview:An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Every solid, liquid, gas and plasma is composed of neutral or ionized atoms. It gives complete information about the electrons related to their size, shape, orientation and how they are filled in orbitals. This course helps the students to understand the nature of chemical bonding on the basis of VBT (Valence Bond Theory), MO (Molecular Orbital) theory and LCAO (Linear Combination of Atomic Orbitals). The contents of this course provide an overview on electronegativity and polarity of bonds. Students will be acquainted about the concept and nature of chemical bonding in homonuclear (H2 to Ne2) and heteronuclear molecules (NO, CO, CN+, CO+, CN- etc.).

This course gives knowledge of calibration of instruments, how to prepare standard solutions of different molarities and normalities.

Objective and expected outcome:The objective of the course is to discuss the structure of atom, concept of orbits and orbitals, how the electrons revolve around the orbits and how they are filled in the orbitals. It will provide knowledge about the elements present in a particular sequence in the periodic table based on their electronic configuration. This course teaches the students how bonds are formed between two atoms using different theories (MO and VBT). After learning these thories, they will get to know about superiority of MO theory for formation of bonds in the molecules and their paramagnetic behavior. Based on the concept of hybridization, students will be able to predict the shape of molecules, their bond angle. Students will learn how to to calculate the lattice energy of ionic compounds using Born – Lande equation and Born - Haber cycle.

The lab related with this course also gives the hands on experience of estimation of elements such as Fe(II) and Fe(III) in a given sample and determination of strength of unknown solution.

BSCH113A GENERAL ORGANIC CHEMISTRY AND CHEMISTRY OF HYDROCARBONS (Credits4)

Overview:This course inculcates the thought process of basic understanding of organic compounds and stereoisomers by giving the fundamental concepts of hybridization and variety of reactions. It also gives an overview on molecular orientation of atoms in three dimensional spaces. Students will get an idea, how these small atoms could easily orient them in a molecule which results in various stereoisomers. The course also covers the chemistry of saturated and unsaturated hydrocarbons.

Objective and Expected Outcome:The objective of the course is to enable students to learn classification and nomenclature of organic compounds. They will appreciate the concept of geometric and optical isomerism and acquire knowledge about the methods of synthesis and reactions of alkanes, alkenes, alkynes, cycloalkanes and aromatic hydrocarbons.This course provides the hands-on experience of how these reaction mechanisms occur and we can relate these reactions with daily life experiences. Combustion of organic compounds such as fuel is a perfect example to notice this type of reaction. This course will enlighten the thoughts of the students regarding the mechanisms of reactions and structure of hydrocarbons. After completion of the course student will be able to critically analyze and relate the nature in terms of reactions.

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BSCH117A STATES OF MATTER (Credits 5)

Overview:States of matter is a key to physical chemists. It is a physical property of matter and it has similar chemical composition and the same chemical properties, regardless of state. Normally every element and compounds form three physical states of matter: solid, liquid and gaseous state, though, other states are equally important. The content of this course provides an overview of various forms of matter. This course offers the formal introduction to the solid state, liquid state and gaseous state. It explains the presence of matter in different stets in terms of balance between intermolecular forces and particle energy. The existences of matter in gaseous state are so wide and strange, students will learn the various laws that govern the behavior of ideal gases and real gases. They will also get the knowledge of various properties of liquids and conditions required for liquefaction of gases.

Objective and expected Outcome: The main objective of the course is to enable the students with the idea that various states of matter are the central science of any physical chemist because of the pivotal role these matters play in the biological and physical sciences, as well as in engineering, agriculture, medicine, and allied health disciplines as every compound is made of these matters only. They will also learn how and why deviations of real gases from ideal gas behavior occurs along with the getting the knowledge of Isotherms of real gases. In other section students will learn the physical properties of liquids, Cleansing action of detergents; Effect of temperature on viscosity of liquids and comparison with that of gases. Lastly the main objective of teaching solid state is to give students an overview of nature of the solid state, Miller indices, X-ray diffraction, Bragg’s equation. This course will enlighten the thoughts of the students regarding basic concepts of kinetic molecular model of a gas and behavior of real gases.

The lab experiments empower students with understanding of physical parameters such as surface tension, density, viscosity of various compounds.

BSCH112A PERIODIC PROPERTIES AND s-BLOCK ELEMENTS (Credits 5)

Overview: Alkali and alkaline earth metals found wide application in daily life. This course deals with basic knowledge of s-block elements, different band theories which are helpful for differentiating between conductors and insulators, solid defects, and types of chemical forces. It also describes the relationship between chemical periodicity and electronic structure of the atom. This course highlights the information about various elements present in the periodic table, their different properties like acids and bases, and variation along groups and periods.

Objective and expected outcome: The main aim of the course is to give insight of long form of periodic table and its classification. The goal of the course is to aware students with the trends in the periodic table like ionic/ atomic radii, oxidation potential, ionization potential, electron enthalpy and electronegativity etc. which gives information about various forms of elements. This course also covers the production of alkali and alkaline earth metals, their uses, their trends in periodic table, and their various types of oxides and halides. After studying this course, students will be able to explain the unique position of hydrogen in the periodic table, its chemistry, industrial production and its bonding; and classification of acids and bases on the basis of Pearson’s concept. Students will be able to explain why first element of alkali and alkaline earth metals shows anomalous behavior with respect to rest of elements and their diagonal relationships.

The lab experiments will help students to acquire the knowledge of Iodo / Iodimetric titrations, and inorganic preparations.

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BSCH114A HALOGENATED HYDROCARBONS AND OXYGEN CONTAINING

FUNCTIONAL GROUPS (Credits 5)

Overview: This course content highlights the structure, stability, methods of synthesis and reactions of arenes and aryl halides. Alkyl halides are among the most versatile compounds in the chemical industry. Small haloalkanes are some of the most commonly used solvents in chemical laboratories; chlorofluorocarbons have seen widespread use as refrigerants and propellants; and compounds containing both Br and F are often used in fire retardants. Within synthetic organic chemistry, they are commonly used in alkylation reactions, radical cascades, and alkyl cross-coupling chemistry.

The course also entails with alcohols, phenols and their acidic strength and chemical properties. It also covers the nomenclature and reactions of ethers and epoxides and their systematic classification. The course will illustrate the method through which hydrolysis of amides and nitration of nitrobenzene can be carried out.

Objective and expected Outcome:These classes of compounds find wide applications in industry as well as in day-to-day life. For instance, have you ever noticed that ordinary spirit used for polishing wooden furniture is chiefly a compound containing hydroxyl group, ethanol. The sugar we eat, the cotton used for fabrics, the paper we use for writing, are all made up of compounds containing –OH groups. Just think of life without paper; no note-books, books, newspapers, currency notes, cheques, certificates, etc. The magazines carrying beautiful photographs and interesting stories would disappear from our life. It would have been really a different world. The reactive nature of primary alkyl chlorides is sometimes exploited in medicinal chemistry and chemical biology.

Halogens containing organic compounds are relatively rare in terrestrial plants and animals. The ocean is the largest known source for atmospheric methyl bromide and methyl iodide. Furthermore, the ocean is also estimated to supply 10-20% of atmospheric methyl chloride, with other significant contributions coming from biomass burning, salt marshes and wood-rotting fungi. Many subsequent chemical and biological processes produce poly-halogenated methane.

It is expected that students will learn about the synthesis, importance, and the reactions of alkyl halide and aryl halides, phenols, alcohols and ethers.

Through this course students will be able to perform acetylation and benzoylation of amines and phenols, oxidation of aldehydes and alcohols etc.

BSCH118A CHEMICAL THERMODYNAMICS (Credits 5)

Overview:This course presents an introduction to Thermodynamics as description of physical phenomena based on the concept of the state of a system and the changes that occur spontaneously or through interaction with other systems. The term system means any identifiable collection of matter that can be separated from everything else by a well-defined surface. From a thermal energy point of view therefore, thermodynamics is the science that dictates what happens in nature and what not and why?

Objective and expected Outcome:Thermodynamics is the study of energy changes accompanying physical and chemical changes. The term itself clearly suggests what is happening -- "thermo", from temperature, meaning energy, and "dynamics", which means the change over time. Thermodynamics can be roughly encapsulated with these topics: Heat and Work. Thermodynamics deals with things like energy, entropy, volume, heat, work, efficiency (ideal), free energy, chemical potential, pressure, temperature etc. The Laws

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of Thermodynamics are important because they control interactions of everything in the universe - regardless of scale. These rules stretch across every form of science known to humankind. Chemical processes were incorporated into the framework of thermodynamics by Gibbs, leading to an understanding of the spontaneity of, and energy exchanged during, chemical reactions and phase changes. The development of statistical mechanics provided a microscopic basis for the theory, explaining how these bulk properties emerge from microscopic system properties (Boltzmann). In this course we shall explain why heat flows from hot to cold bodies, why the air becomes thinner and colder at higher altitudes, why the Sun appears yellow whereas colder stars appear red and hotter stars appear bluish-white, why it is impossible to measure a temperature below -273 C, why there is a maximum theoretical efficiency of a power generation unit which can never be exceeded no matter what the design, why high mass stars must ultimately collapse to form black-holes, and much more. There are two methods of describing the thermodynamic behavior of multi-component systems: one of them is based on excess functions and another on the equation of state. The excess function/property provides the deviation from ideal behavior of a liquid or gas mixture. It can also inform about the type molecular interactions, i.e., attraction or repulsion, related to the state of pure compounds before mixing.

Through the above mentioned questions, students will understand the importance of thermodynamics and gain the knowledge of theories and concepts behind this.

The lab experiments are designed so as to acknowledge the students with the concept of enthalpy related to the various phenomenon observed in daily life such as neutralization, and sublimation etc.

6.5 Syllabi of Courses specific to B.Sc.(Hons.)Physics

BSPH131A MATHEMATICAL PHYSICS-I (Credits 6)

Overview:Differential equations are an important mathematical tool which can be used to describe many applications to everyday life and technology. Differential equations can be used to model various problems from population dynamics to quantum mechanics. Knowledge of Vectors and Orthogonal Curvilinear coordinates systems is also very important for solving many problems in Physics. Uncertainty and randomness occur in many aspects of our daily life and having a good knowledge of probability helps us make sense of these uncertainties. This course aims to develop the basics of modeling of real life problems using these mathematical tools.This course covers basics of vectors, vector differentiation and integration, orthogonal curvilinear coordinate systems, differential equations and probability theory.

Objective and Expected Outcome:Students will be able to identify the difference between order/degree, linear/non linear, ordinary/partial, homogeneous/non homogeneous nature of differential equations. They will learn various methods and techniques for solving differential equations such as separation of variable, Integrating factor method, Variation of parameters and D operator method etc. Apart from this, they will be able to apply differential equations to model various problems in Physics for example electrical circuits, radioactive decay, simple harmonic motion, bending of beams, wave propagation etc. Students will also get acquainted with Vector Calculus (Dot product, cross product, vector differentiation, Integration, Stoke’s theorem and Gauss Divergence theorem), Orthogonal Curvilinear coordinates system and probability theory.

BSPH133A MECHANICS (Credits 6)

Overview:Every motion, either linear or rotational is governed by certain laws. Mechanics deals with these

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laws and formulates them in a scientific manner. Linear motion is a translational motion in a straight line. The concept of ‘force’ is fully explained by Newton through his laws of motion. Force is responsible for linear acceleration while torque for angular acceleration. The basic ideas of state of rest and uniform motion were studied by various philosophers. According to Aristotle (384-322 BC), a constant force has to be applied on a body so as to keep it in motion with constant velocity. Later on, Galileo (1564-1642 AD) stated that no force is required for a body to move with uniform velocity. Newton (1642-1727 AD) was the first person who formulated the laws differentiating ‘state of rest’ and ‘state of uniform motion’. Newton’s notion of space as ‘Absolute space’, isotropic nature for rotational invariance and homogeneity for translational invariance led to understand the laws of motion in inertial frame of reference. Any accelerated frame of reference is a non-inertial frame.

This course is especially appropriate for students planning to specialize in physical science or engineering. The course explores topics such as kinematics; Newton's laws of motion; work, energy and power; systems of particles and linear momentum; circular motion and rotation; and oscillations and gravitation. Introductory differential and integral calculus is used throughout the course.

Objective and Expected Outcome:Students will be able to articulate and describe relative motion, inertial and non-inertial reference frames, and parameters defining the motion of mechanical systems and their degrees of freedom, study of the interaction of forces between solids in mechanical systems, Centre of mass and inertia tensor of mechanical systems, application of the vector theorems of mechanics and interpretation of their results, Newton’s laws of motion and conservation principles, introduction to analytical mechanics as a systematic tool for problem solving, use of mechanical simulation software.

On successful completion of this course, students are expected to be able to interpret and solve problems based on the laws of mechanics and force and equilibrium concepts, perform calculations related to mass moment of inertia, evaluate forces of friction and the principles of rigid body dynamics.

BSPH132A ELECTRICITY AND MAGNETISM (Credits 6)

Overview:The course gives an overview and understanding of basic physics, with moderate use of mathematical formalism. Topics include concepts in electricity and magnetism together with their relationship to practical applications.

The major concepts covered are: - The abstraction from forces to fields using the examples of the electric and magnetic fields, with some applications vis-a-vis the connection between conservative forces and potential energy, how charges move through electric circuits, the close connection between electricity and magnetism, leading to the discovery of electromagnetic waves. - the integral form of Maxwell's Equations etc.

Objective and Expected Outcome:The objective of the course is to develop a basic understanding of electric and magnetic fields in free space: definitions, units, laws and rules as well as interesting things connected with discoveries and discoverers of crucial phenomena.

After completion of this course, students will:

• Apply knowledge of electricity and magnetism to explain natural physical processes and related technological advances.

• Use an understanding of calculus along with physical principles to effectively solve problems encountered in everyday life, further study in science, and in the professional world.

• The student can solve problems with moderate mathematical complexity related to

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electric and magnetic force and field, electric charge, electric potential, current, voltage and resistance, capacitors, electromagnetic waves, reflection, refraction, interference and diffraction.

• Design experiments and acquire data in order to explore physical principles, effectively communicate results, and critically evaluate related scientific studies.

• Assess the contributions of physics to our evolving understanding of global change and sustainability while placing the development of physics in its historical and cultural context.

BSPH134A WAVES AND OPTICS (Credits 6)

Overview:The physics and mathematics of wave motion underlies many important phenomena. The water wave on the sea, the vibration of a violin string, and the quantum mechanical wave associated with an electron can all be described in a similar way. Light too, often displays properties that are wave-like. We will start the course looking at “ray” optics, but then pause for a general treatment of waves of all types. We will start this waves section by reviewing ideas of oscillations and simple harmonic motion and go on to look at the physics of travelling and standing waves i.e. wave motion. We will apply these ideas to various types of wave and see how all-pervading this topic is in physics. Optics is the study of light and its uses. Light has long captured the fascination of humankind like Why should light bend upon entering water? Why does light spread out after passing through a narrow gap? How does light travel to us from the sun, through the void of space? These sorts of questions have ensured that optics has a long and engaging history. Soin this lecture course we will look at basic ideas of light propagation, interference and diffraction of light, Polarization, and some of the many uses to which light is put.

Objective and Expected Outcome:Students will acquire skills allowing the student to identify and apply formulas of optics and wave physics using course literature. After the completion of course students will be able to identify and illustrate physical concepts and terminology used in optics and to be able to explain them in appropriate detail. They will be able to apply their knowledge to make approximate judgements about optical and other wave phenomena when necessary.

They can acquire skills allowing them to organize and plan simpler laboratory course experiments and to prepare an associated oral and written report.

6.6 Syllabi of Courses specific to B.Sc. (Hons.)Mathematics

BSMA133A CALCULUS (Credits 5)

Overview:This is considered a first course in calculus, primarily for students intending to continue to advanced courses in calculus, and mathematics in general. Students conduct a detailed study of differential calculus and its applications, and are introduced to antiderivatives.

Objective and Expected Outcome:Upon the completion of this course, the student will be able to:

• Know what a function is and know the four ways to represent a function.• Appreciate how functions can be used to model situations such as population growth,

tides, vibrating springs, and gas emissions.• Make new functions from old by transforming, combining, and composing.• Know when a function has an inverse and how to find the inverse.• Know and sketch the members of the catalogue of essential functions.

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• Understand the concepts of a limit and one-sided limits, continuity, and differentiability.• Determine limits numerically, algebraically, and from a graph.• Determine limits of indeterminate forms, using L' Hospital's Rule.• Understand the concepts of continuity and differentiability and the relationship between

them.• Know the differentiation formulas for polynomial, rational, trigonometric, inverse

trigonometric, exponential, and logarithmic functions.• Apply the rules and techniques of differentiation to any combination of functions.• Apply the derivative to solve a variety of problems (related rates problems, optimization

problems, curve sketching).• Use the derivative to find the linear approximation of a function.• Use Newton's method to find the roots of a function.• Understand the concept of the antiderivative, and find antiderivatives.

LEARNING OUTCOMES:• Understanding of the ideas of limits and continuity and an ability to calculate with them

and apply them. • Improved facility in algebraic manipulation. • Fluency in differentiation.• Fluency in integration using standard methods, including the ability to find an appropriate

method for a given integral. • Facility in applying Calculus to problems including curve-sketching, areas and volumes. • Understanding the ideas of infinite series including Taylor approximations. • Understanding the ideas of differential equations and facility in solving simple standard

examples.

BSMA137A ALGEBRA (Credits 4)

Overview:Algebra is designed to give students a foundation for all future mathematics courses. The fundamentals of algebraic problem-solving are explained. Students will explore the basic concepts of matrices, relation between the roots and coefficients of general polynomial equation in one variable, Nature of roots by inspection of change of sign of equations. Throughout the course the student learns how to apply the concepts in real-life situations.

Objective and Expected Outcome: During this course the student will be able to find the rank, Eigen values of matrices and solve the homogeneous and non-homogeneous systems, solution of cubic and biquadratic equations.

Upon completion of this course, students should be able to understand mathematical concepts, symbols and procedures and are able to apply them to real world situations. Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations including those in real-life contexts. Select and apply appropriate inquiry and mathematical problem solving techniques in recognize patterns.

The main objective of this program is to cultivate a mathematical aptitude and nurture the interests of the students towards problem solving aptitude. Further, it aims at motivating the young minds for research in mathematical sciences and to train computational scientists who can work on real life challenging problems. It further aims at motivating the students to join teaching profession.

DISCIPLINE ELECTIVE I:

BSMA136A ANALYTICAL GEOMETRY (Credits 4)

Overview:

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This course will introduce to the analytic geometry with examples from real life and various sciences. In selecting such problems for our examples and exercises we highlighted this motivation by references to applications in the social, business, and life sciences. The course was prepared with three related objectives: concreteness, motivation and applicability.

Objective and Expected Outcome:This is a beginning course in plane analytic geometry emphasizing the correspondence between geometric curves and algebraic equations. This correspondence makes it possible to reformulate problems in geometry as equivalent problems in algebra, and vice versa. Curves studied include straight lines, circles, parabolas, ellipses, and hyperbolas. Coordinate transformations, polar coordinates, and parametric equations are also studied. The course assumes a sound background in algebra, geometry, and trigonometry.

LEARNING OUTCOMES: • Students will be able to write equations of lines, circles, and conics in 2-space and to

identify these curves from their equations. • Students will be able to write equations of lines and planes in the 3-space and to identify

lines and planes from their equation. • Students will be able to measure the distances between points, lines, and planes • Students will be able to use vectors in 2- and 3-space to solve problems. • Students will be able to use rectangular and polar coordinates in 2-space.• Students will be able to use rectangular, cylindrical, and spherical coordinates in 3-

space. • Students will be able to perform translations and rotations in 2-space. • Determine equations of a circle, parabola, ellipse and hyperbola; cylinder, cone, ellipsoid,

hyperboloids and paraboloids.A student who has studied and learned the material should be able to: 1. Solve problems involving lengths and distances in the plane, including midpoint and point-of-division formulas. 2. Demonstrate understanding of the notions of slope and inclination of lines, including angles between lines, parallel lines, and perpendicular lines. 3. Recognize the relationship between equations in two variables and graphs in the plane and use the equations to find pertinent information such as points of intersection, and intercepts. 4. Perform arithmetical and geometric operations involving vectors in the plane. 5. Use vectors to solve geometric and physical problems. 6. Sketch graphs of and discuss relevant features of curves in the plane determined by certain equations (including lines, circles, parabolas, ellipses, hyperbolas, polynomial functions, rational functions, and features such as slope, inclination, center, radius, vertices, foci, axes, eccentricity, intercepts, asymptotes). 7. Determine equations of curves when given information that determines the curves. 8. Perform translations and rotations of the coordinate axes to eliminate certain terms from equations. 9. Model real world situations with equations of conics. 10. Use the polar coordinate system, relate it to the rectangular coordinate system, and graph equations using polar coordinates. 11. Sketch graphs in the plane determined by parametric equations by direct sketching as well as elimination of the parameter to obtain a rectangular equation.


BSMA336A NUMBER THEORY (Credits 4)

Overview:Number theory is a rich and abstract branch of mathematics which explores the fundamental properties of our number system. Number Theory, branch of mathematics concerned with properties of the positive integers . Sometimes called “higher arithmetic,” it is among the oldest and most natural of mathematical pursuits.

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Number theory has always fascinated amateurs as well as professional mathematicians. In contrast to other branches of mathematics, many of the problems and theorems of number theory can be understood by laypersons, although solutions to the problems and proofs of the theorems often require a sophisticated mathematical background.

Until the mid-20th century, number theory was considered the purest branch of mathematics, with no direct applications to the real world. The advent of digital computers and digital communications revealed that number theory could provide unexpected answers to real-world problems. At the same time, improvements in computer technology enabled number theorists to make remarkable advances in factoring large numbers, determining primes, testing conjectures, and solving numerical problems once considered out of reach.

Objective and Expected Outcome:Modern number theory is a broad subject that is classified into subheadings such as elementary number theory, algebraic number theory, analytic number theory, geometric number theory, and probabilistic number theory. These categories reflect the methods used to address problems concerning the integers. Algebraic geometry and algebraic number theory, which provide many natural examples of commutative rings, have driven much of the development of commutative ring theory, which is now, under the name of commutative algebra, a major area of modern mathematics. Because these three fields (algebraic geometry, algebraic number theory and commutative algebra) are so intimately connected it is usually difficult and meaningless to decide which field a particular result belongs to. For example, Hilbert's Nullstellensatz is a theorem which is fundamental for algebraic geometry, and is stated and proved in terms of commutative algebra. Similarly, Fermat's last theorem is stated in terms of elementary arithmetic, which is a part of commutative algebra, but its proof involves deep results of both algebraic number theory and algebraic geometry.


BSMC119A MATHEMATICAL FINANCE (Credits 4)

Overview:Mathematical finance, also known as quantitative finance, is a field of applied mathematics, concerned with mathematical modeling of financial markets. Generally, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory.

This four module course demonstrates how a number of financial mathematics formulas can be used to conduct detailed analysis on a set of data and/or variables.

Objective and Expected Outcome: We explore the concept of the “time value of money”. The module focuses on how to calculate present values and future values using compounding and discounting techniques. The module then goes on to outline how the present values of annuities, perpetuities, and growing perpetuities can be calculated. Each concept is reinforced with practical and applied exercises and case studies. By the end of this module, you will have a solid understanding of how discounted cash flows techniques are used to evaluate future cash flows.

• Understand the concept of the time value of money• Explain terms such as present value, future value, NPV, DCF, annuities, and perpetuities• Use DCF techniques to calculate present values• Calculate the present value of cash flow streams such as annuities and perpetuities

Study of the topics of the course will enable the students to

• Provide active and practical use of mathematics, which includes interrelated financial

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topics.• Provide an experience of formulating finance problems into computational problems. • Provide an illustration of the role of optimization in computational finance such as single

and multi-period mean-variance portfolio management.

OPEN ELECTIVE I:

IIIT107A ART OF LOGIC AND PROGRAMMING (Credits 4)

Overview:Considering implementation and practicing logics and connections for a problem statement seems to be need of today's world. To achieve an outcome, programmer should be clear with logics, hardware requirement and its related consequences to other units of the system in whole. This subject will help student to develop and understand a concept of problem statement in detail and further implementing solution by logical justification and decisions.

Objective and Expected Outcome:During course of journey of “Art of Logics”, student will initiate from basic of elementary programming language. Which will further step forward to its application areas and reflection in practical day to day life. Inheriting knowledge of elementary programming language student will be in state to develop anstand alone project based on concept of structuring primitive and non- primitive data. While going through course, student will learn about array, stack, queues, trees and graphs and its related application areas.

This course will initiate new and creative imaginations. After completing the course, students will be able to deal with dynamic situations for decision making and problem solving on a real-world phenomenon.

BSMA135A VECTOR ANALYSIS (Credits 4)

Overview:This paper presents results from vector analysis that pertains to integration. A major reason to study vector functions over a surface is to measure flux. Flux is an important concept in electricity and magnetism. An intuitive way to visualize flux is the passage of a fluid through a membrane. The divergence and curl are two of the most important operators in vector calculus. One way of presenting them is to define them in terms of mathematical formulas. The line integral of a vector field over a path gives the tendency of the vector field to follow that path. This is often called the circulation of the vector field along the path. A positive circulation indicates the movement with the direction of the vector field.

Objectives and expected outcome: By the end of the module the student should understand:

• Define double integrals over rectangles• Compute iterated integrals • Define and compute double integrals over general regions • Compute double integrals in polar coordinates • Find moments and centers of mass using double integrals• Compute triple integrals in Cartesian coordinates, cylindrical coordinates and spherical • coordinates• Apply triple integrals to find volumes and center of mass• Change variables in multiple integrals • Define vector fields • Calculate line integrals along piecewise smooth paths; interpret such quantities as work

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done by a force • Use the fundamental theorem of line integrals • Use Green’s theorem to evaluate line integrals along simple closed contours on the

plane • Compute the curl and the divergence of vector fields • Compute the area of parametric surfaces in 3-dimensional space • Compute surface integrals • Apply Stokes’ theorem to compute line integrals along the boundary of a surface • Use Stokes’ theorem to give a physical interpretation of the curl of a vector field • Use the divergence theorem to give a physical interpretation of the divergence of a

vector field

BSMA138A GROUP THEORY (Credits 4)

Overview:This course covers the theoretical aspects of groups. However, with the development of computing in the last several decades, applications that involve modern algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing mathematics. Their applications such as coding theory and cryptography have grown significantly. However, one of the major problems in teaching modern algebra course is that for many students it is their first encounter with an environment that requires them to do rigorous proofs. Such students often find it hard to see the use of learning to prove theorems and propositions; applied examples help the instructor provide motivation.

Objective and Expected Outcome:In real life, however, algebra merges into all other areas as a tool. Whenever life throws a mathsproblem at you, for example when you have to solve an equation or work out a geometrical problem, algebra is usually the best way to attack it. The equations you are learning about now are the ones that you’re most likely to come across in everyday life. This means that knowing how to solve them is very useful. If you’re planning to go into computer programming, however, the algebra you’ll need is more complicated and now’s the time to make sure you get the basics.

This course starts by introducing the basics of group theory including symmetric group etc.

Group theory, the ultimate theory for symmetry, is a powerful tool that has a direct impact on research in robotics, computer vision, computer graphics and medical image analysis.

BSMA140A ADVANCED CALCULUS (Credits 5)

Overview:This is a first course in advanced calculus. The focus will be on functions of two and three variables, and using calculus to analyze the geometry of curves and surfaces in three-dimensional space. The official description from the Department of Mathematics is as follows: Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces.Partial derivatives.Multiple integrals.Vector Calculus.Theorems of Green, Gauss, and Stokes.

Objective and Expected Outcome:The objective of this course to introduce functions of several variable to a student after he has taken a course in one variable calculus. The course will introduce partial derivatives and several of its consequences and will introduce double and triple integrals along with line integrals which are fundamental to all streams where calculus can be used.

After reading this course a student will be able to calculate partial derivatives, directional derivatives, and extreme values and can calculate double, triple and line integrals. He will have

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idea of basic vector calculus including green’s theorem, divergence theorem and stokes theorem. He can take courses in calculus on manifolds, Differential geometry and can help in numerical computations involving several variables.

After completing this course, students should have developed a clear understanding of the fundamental concepts of multivariable calculus and a range of skills allowing them to work effectively with the concepts.

The basic concepts are:

• Derivatives as rates of change, computed as a limit of ratios• Integrals as a 'sum,' computed as a limit of Riemann sums

The skills include:

• Fluency with matrix algebra, including the ability to put systems of linear equation in matrix format and solve them using matrix multiplication and the matrix inverse.

• An understanding of a parametric curve as a trajectory described by a position vector; the ability to find parametric equations of a curve and to compute its velocity and acceleration vectors.

• A comprehensive understanding of the gradient, including its relationship to level curves (or surfaces), directional derivatives, and linear approximation.

• The ability to compute derivatives using the chain rule or total differentials.• The ability to set up and solve optimization problems involving several variables, with or

without constraints.• An understanding of line integrals for work and flux, surface integrals for flux, general

surface integrals and volume integrals. Also, an understanding of the physical interpretation of these integrals.

• The ability to set up and compute multiple integrals in rectangular, polar, cylindrical and spherical coordinates.

• The ability to change variables in multiple integrals.• An understanding of the major theorems (Green's, Stokes', Gauss') of the course and of

some physical applications of these theorems.

DISCIPLINE ELECTIVE II:

BSMA146A GRAPH THEORY (Credits 4)

Course Description: What do transportation systems, social networks, the Web, power grids, financial markets and many biological systems have in common? They are examples in which we seek to understand not only the entities which interact, but also the patterns of interaction between the entities. Graph theory is rooted in mathematics and computer science as it serves a mathematical model for any system involving a binary relations.

This is an introductory course on the theory of graphs. The primary focus is on understanding graph properties, learning common proof techniques and studying relations between various graph parameters. Topics covered in this course include: graphs as models, paths, cycles, directed graphs, trees, spanning trees, matchings (including stable matchings), network flows, and graph coloring (including scheduling applications). Various graph algorithms are also discussed along with its analysis.

In this course, among other intriguing applications, we see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We also study Ramsey Theory which proves that in a large system, complete disorder is impossible!

Objective and Expected Outcome:

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Upon completing this course, the students will be able to: know some important classes of graph theoretic problems; formulate and prove central theorems about trees, matching, connectivity, colouring and planar graphs; describe and apply basic algorithms and use graph theory as a modelling tool. The students will have intimate knowledge about how the graph theory play an important role to solve the technology driven and research oriented problems.


BSMA327A DYNAMICS (Credits 4)

Overview:The motive that guides this course is the unveiling of facts and information describing the motion of an object.

The motion of an entity or a body connects to a real physical system. A rigid body is formed by a large number of particles and this body has six degrees of freedom in the 3-dimensional space - three translations and three rotations about the x, y, and z-axes. Dynamics helps us to describe the motion of a rigid body, and this description is applied to a specific problem. Let us consider a simple example for the purpose of illustration. If a drum starts rotating at time with initial angular velocity ꙍ, then how many times will it rotate until it comes to stop?

This course will enable students to learn how laws of physics and mathematics are used to describe the motion of objects in real-world situations.

Objective and Expected Outcome:The discipline that determines the velocity and position of an object under the action of forces is considered as dynamics. This course starts with the concepts of position, displacement, velocity and acceleration in order to understand the motion of particles along a straight line or a curved path. The course proceeds further with a deeper look at Newton’s second law, constraints and degrees of freedom, and units of measurements. Building models and free-body diagrams are the key concepts of this learning module. In addition, students shall encounter problems based on the principles of work, energy and power, and the general motion of a rigid body.

This course serves students by implementing precise mathematics and strengthening deep understanding of the concepts, and that will help them throughout their professional and educational careers.


BSMC226A PORTFOLIO OPTIMIZATION (Credits 4)

Overview:Analyzing security before committing funds into it is the most important and primitive step one starts with. The analysis of various financial instruments traded in the market is security analysis which determines the real worth of the security. We see its application in normal life routines as well, like we make sure the price what we pay for any item we purchase is worth it or not. The stock which is bought should be assessed in light of all past, present and hidden information. It refers to theories like Portfolio theory, Efficient Market theory, CAPM, APT and brings its relevance in context to selecting asset for building a portfolio. The investor puts his investments in group of assets to make sure the portfolio he makes gives the maximum return and carries less risk. The portfolio construction which in other words is diversification is built optimally and managed from time to time and revised if the need arises.

Objective and Expected Outcome:

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The course would help the learner to fundamentally and technically study the security or any stock before considering it for investments. Since the investor makes a portfolio and makes investment in a group of assets, the learner studies to select the securities in a way that would combat the risk of other security keeping the portfolio theory as the base. The beauty of the course is that it enables one to plan investments for oneself as well as act as financial advisors for others. The students learn to align the securities with the market index to get the maximum and learn the significance of beta in calculating the asset 2price. The investment objective and the risk appetite of the individual differs from others and this acts as a stepping stone before suggesting or considering the stock for investments and the course provide a deep insights into this context.The course will make the learner to understand how securities are analyzed and a portfolio is built, managed/revised to enjoy the optimum return from the investment in the given risk. They would learn to assess the security in context to its risk and return and compare it with other securities and with the market.

OPEN ELECTIVE II:

IIIT102A FUNDAMENTALS OF INNOVATION AND ENTREPRENEURSHIP (Credits 4)

Overview:This course examines successful strategies, business models, frameworks, funding, barriers and risks for introducing break-through products and services. Topics include: Transforming Ideas to Opportunities, Entrepreneurship Business Entities, Being a successful entrepreneur and different Sources of Investment.

Objective and Expected Outcome:Do you want to be a young entrepreneur like Tilak Mehta 13 year old teenager of Mumbai and CEO of Paper n Parcel or Ritesh Agarwal CEO of OYO Rooms ? Do you want to build your own future? Develop your own ideas? Set up your own company or social enterprise? Make a difference in the world. This course aims at Creating new businesses, capturing new markets, enhancing organizational effectiveness occur through innovation, transforming processes - or both. New technologies, processes, competition and globalization compel entrepreneurs and existing firms to distance from the familiar and foster innovation and agility. Students will develop skills and insights for evaluating, articulating, refining, and pitching a new product or service, either as a start-up business or a new initiative within an existing firm. This course is appropriate for all students interested in innovation and design as necessary components of new businesses today

Project or Business Plan“Demand are dynamic to be aware of dynamical changes” . This Project is based on real world problem:

“India E-Waste Management Market Forecast & Opportunities, 2019” • E-Waste Management Market Size, Share & Forecast in India• Segmental Analysis – IT & Telecom, Household Appliances & Consumer Electronics• Changing Market Trends & Emerging Opportunities• Policy and Regulatory Landscape• Strategic Recommendations & Competitive Landscape

Why this study has to be conducted?• To gain an in-depth understanding of E-Waste Management market in India• To identify the on-going trends and anticipated growth in the coming years• To help industry consultants, E-Waste management players and other stakeholders to

align their market-centric strategies

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• To obtain research based business decision and add weight to presentations and marketing material

• To gain competitive knowledge of leading players• To avail 10% customization in the report without any extra charges and get the research

data or trends added in the report as per the buyer’s specific needsMethodology The information contained in this study will be based upon both primary and secondary sources. Primary research included interviews with E-Waste Management and Recycling companies and NGOs. Secondary research included an exhaustive search of relevant publications like company annual reports, financial reports and proprietary databases.

References:• The education of Millionaires: Michael Ellsberg• The $100 startup : Chris Guillebeau• The Greatest Miracle in the World: by OgMandino• The Age of Entrepreneurship Business Owners, Self-employment and Corporations

since 1851 Robert J. Bennett, University of Cambridge, UK, Harry Smith, Gill Newton, Cary van Lieshout and PieroMontebruno

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men

t and

C

omm

unic

atio

n Sk

ills

35

BSC

S112

AO

bjec

t Ori

ente

d Pr

ogra

mm

ing

5

2022

1B

SMA

323A

Met

ric

Spac

es4

1B

SMA

324A

Rie

man

n In

tegr

atio

n an

d Se

ries

of

Func

tions

4

2B

SMA

325A

Com

plex

Ana

lysi

s5

2B

SMA

326A

Ope

ratio

nal R

esea

rch

5

3B

SMA

331A

Num

eric

al A

naly

sis

53

BSM

A34

2AM

athe

mat

ical

Sta

tistic

s4

4B

SMA

333A

Des

crip

tive

Stat

istic

s5

4D

isci

plin

e E

lect

ive

VI

4

5D

isci

plin

e E

lect

ive

V4

5B

SMA

354A

Proj

ect

5

2322

1B

SMA

136A

Ana

lytic

al G

eom

etry

41

BSP

H12

0AC

onde

nsed

Mat

ter P

hysi

cs4

2B

SMA

336A

Num

ber T

heor

y4

2B

SCH

120A

Fund

amen

tals

of C

hem

istr

y an

d W

ater

Pro

cess

es4

3B

SMC

119A

Mat

hem

atic

al F

inan

ce4

3II

IT10

1AH

arne

ssin

g th

e Po

wer

of t

he W

eb a

s a

Kno

wle

dge

Dev

ice

4

4II

IT10

7AA

rt o

f Log

ic a

nd P

rogr

amm

ing

4

1B

SMA

146A

Gra

ph T

heor

y4

2B

SMA

327A

Dyn

amic

s4

1B

SPH

217A

App

licat

ions

of M

ater

ials

4

3B

SMC

226A

P

ortf

olio

Opt

imiz

atio

n4

2B

SCH

207A

Tec

hnic

al In

terf

ace

of C

hem

istr

y4

3II

IT10

2AFu

ndam

enta

ls o

f Inn

ovat

ion

and

Ent

repr

eneu

rshi

p4

1B

SMA

225A

Prob

abili

ty T

heor

y4

4II

IT10

4AU

nder

stan

ding

the

Pow

er o

f Dat

a

4

2B

SMA

227A

Boo

lean

Alg

ebra

and

Aut

omat

a T

heor

y4

3B

SES3

09A

Eco

nom

etri

cs4

1B

SMA

221A

Stat

ics

4

2B

SMA

332A

Com

bina

tori

al M

athe

mat

ics

4

Third

TO

TA

LT

OT

AL

Ele

ctiv

es (C

hoos

e an

y on

e fr

om e

ach)

Dis

cipl

ine

Ele

ctiv

e I

Ope

n E

lect

ive

Cou

rse

I

Dis

cipl

ine

Ele

ctiv

e II

Ope

n E

lect

ive

Cou

rse

II

Dis

cipl

ine

Ele

ctiv

e II

I

Dis

cipl

ine

Ele

ctiv

e IV

AN

NE

XU

RE

III

B.S

c. (H

) Mat

hsY

ear

2019

- 20

22 (S

chem

e of

stu

dies

)SB

AS

OD

D S

EM

EST

ER

E

VE

N S

EM

EST

ER

First

TO

TA

LT

OT

AL

Second

TO

TA

LT

OT

AL

35

Yea

rSN

Cou

rse

Cod

eC

ours

e T

itle

CSN

Cou

rse

Cod

eC

ours

e T

itle

C

1B

SMA

133A

Cal

culu

s5

1B

SMA

135A

Vec

tor A

naly

sis

4

2B

SMA

137A

Alg

ebra

4

2B

SMA

138A

Gro

up T

heor

y4

3D

isci

plin

e E

lect

ive

I4

3B

SMA

140A

Adv

ance

d C

alcu

lus

5

4O

pen

Ele

ctiv

e C

ours

e I

44

Dis

cipl

ine

Ele

ctiv

e II

4

5B

SCH

125A

Env

iron

men

tal S

tudi

es3

5O

pen

Ele

ctiv

e C

ours

e II

4

6B

SCS1

02A

Info

rmat

ion

Tec

hnol

ogy

Fund

amen

tals

46

BSE

L101

AC

omm

unic

atio

n Sk

ills

5

2426

1B

SMA

134A

Ord

inar

y D

iffe

rent

ial E

quat

ions

51

BSM

A21

8ASp

ecia

l fun

ctio

ns a

nd In

tegr

al

Tra

nsfo

rms

4

2B

SMA

217A

Rea

l Ana

lysi

s4

2B

SMA

219A

Part

ial D

iffe

rent

ial E

quat

ions

5

3B

SMA

223A

Rin

g T

heor

y4

3B

SMA

220A

Line

ar A

lgeb

ra4

4D

isci

plin

e E

lect

ive

III

44

Dis

cipl

ine

Ele

ctiv

e IV

4

5B

SEL2

17A

Pe

rson

ality

Dev

elop

men

t and

C

omm

unic

atio

n Sk

ills

35

BSC

S112

AO

bjec

t Ori

ente

d Pr

ogra

mm

ing

5

2022

1B

SMA

323A

Met

ric

Spac

es4

1B

SMA

324A

Rie

man

n In

tegr

atio

n an

d Se

ries

of

Func

tions

4

2B

SMA

325A

Com

plex

Ana

lysi

s5

2B

SMA

326A

Ope

ratio

nal R

esea

rch

5

3B

SMA

331A

Num

eric

al A

naly

sis

53

BSM

A34

2AM

athe

mat

ical

Sta

tistic

s4

4B

SMA

333A

Des

crip

tive

Stat

istic

s5

4D

isci

plin

e E

lect

ive

VI

4

5D

isci

plin

e E

lect

ive

V4

5B

SMA

354A

Proj

ect

5

2322

1B

SMA

136A

Ana

lytic

al G

eom

etry

41

BSP

H12

0AC

onde

nsed

Mat

ter P

hysi

cs4

2B

SMA

336A

Num

ber T

heor

y4

2B

SCH

120A

Fund

amen

tals

of C

hem

istr

y an

d W

ater

Pro

cess

es4

3B

SMC

119A

Mat

hem

atic

al F

inan

ce4

3II

IT10

1AH

arne

ssin

g th

e Po

wer

of t

he W

eb a

s a

Kno

wle

dge

Dev

ice

4

4II

IT10

7AA

rt o

f Log

ic a

nd P

rogr

amm

ing

4

1B

SMA

146A

Gra

ph T

heor

y4

2B

SMA

327A

Dyn

amic

s4

1B

SPH

217A

App

licat

ions

of M

ater

ials

4

3B

SMC

226A

P

ortf

olio

Opt

imiz

atio

n4

2B

SCH

207A

Tec

hnic

al In

terf

ace

of C

hem

istr

y4

3II

IT10

2AFu

ndam

enta

ls o

f Inn

ovat

ion

and

Ent

repr

eneu

rshi

p4

1B

SMA

225A

Prob

abili

ty T

heor

y4

4II

IT10

4AU

nder

stan

ding

the

Pow

er o

f Dat

a

4

2B

SMA

227A

Boo

lean

Alg

ebra

and

Aut

omat

a T

heor

y4

3B

SES3

09A

Eco

nom

etri

cs4

1B

SMA

221A

Stat

ics

4

2B

SMA

332A

Com

bina

tori

al M

athe

mat

ics

4

Third

TO

TA

LT

OT

AL

Ele

ctiv

es (C

hoos

e an

y on

e fr

om e

ach)

Dis

cipl

ine

Ele

ctiv

e I

Ope

n E

lect

ive

Cou

rse

I

Dis

cipl

ine

Ele

ctiv

e II

Ope

n E

lect

ive

Cou

rse

II

Dis

cipl

ine

Ele

ctiv

e II

I

Dis

cipl

ine

Ele

ctiv

e IV

AN

NE

XU

RE

III

B.S

c. (H

) Mat

hsY

ear

2019

- 20

22 (S

chem

e of

stu

dies

)SB

AS

OD

D S

EM

EST

ER

E

VE

N S

EM

EST

ER

First

TO

TA

LT

OT

AL

Second

TO

TA

LT

OT

AL

3B

SCS3

12A

Info

rmat

ion

and

Net

wor

k Se

curi

ty4

1B

SMA

334A

Dif

fere

ntia

l Geo

met

ry4

2B

SMA

335A

App

licat

ions

of A

lgeb

ra4

3B

SCS2

14A

T

heor

y of

Com

puta

tion

4

1B

SMA

344A

Bio

-Mat

hem

atic

s 4

2B

SMA

338A

Mat

hem

atic

al M

odel

ling

4

3B

SMC

325A

B

anki

ng a

nd In

sura

nce

Ope

ratio

ns4

Dis

cipl

ine

Ele

ctiv

e V

Dis

cipl

ine

Ele

ctiv

e V

I

Tot

al C

redi

ts [

C]

137

Stud

ent c

an c

hoos

e tw

o no

n cr

edit

cour

ses

(2 h

ours

per

wee

k), o

ne in

odd

sem

este

r an

d on

e in

eve

n se

mes

ter

duri

ng th

e en

tire

dura

tion

of

Prog

ram

me

from

the

pool

of c

ours

es p

rovi

ded

by th

e un

iver

sity

.

SCH BASIC A APPI SCIC Science.… · 4 3.1 B. Sc. (Hons.) Chemistry This course aims to impart...

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Transcript of SCH BASIC A APPI SCIC Science.… · 4 3.1 B. Sc. (Hons.) Chemistry This course aims to impart...