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University of TehranCollege of Science

Department of Mathematics, Statistics and Computer Science

Graduate Program in Computer Science

1- Introduction

The field of computer science forms the theoretical basis for all computer-related disciplines. This field includes theoretical discussions of computers in different majors and branches, and is closely related to pure mathematics, theoretical physics, and biology. The topics of this discipline extend and deepen the computer structures with mathematical and theoretical viewpoints, and provide theoretical infrastructure for computer-related disciplines. Of course, the growth of theoretical structures, leads to more usage of computer applications in technology.The Master and Ph.D. degrees has six majors of Algorithm, Logic and Computation, Artificial intelligence, Bioinformatics, Data science, Computational Combinatorics and Formal methods. Students in the master program gain a growing degree of knowledge in the field of computer science and by doing specialized researches, acquire the necessary scientific and practical skills. The Ph.D. program in Computer Science is an educational and research program, and in this program, the invention, innovation and development of computer science knowledge have particular importance and constitute the special mission of the students. The goal of this program is to train professional persons who have received the necessary training in computer science and have acquired the necessary skills in this field and, while deepening in several specialized courses, can provide international research work.

2. The length of programs and the form of the educational system

A. Master program

The total number of units is 28, of which 20 units consist of 5 courses, each will be worth 4 units, and include a seminar course of 2 units and a dissertation is 6 units.

The number of units for completing this program is 28 units.

1. The Specialized courses for all majors are 10 units (Table 1)2. Optional courses of major are 12 units (Tables 2 to 7)3. Thesis includes 6 units

B. Ph.D. program

The total number of units is 36 units, of which 16 units are courses and 20 units of the doctoral thesis. The Ph.D. program in computer science is divided into two educational and research stages.

At the educational stage, the student must complete 16 course units.

1. The Specialized courses of major are 8 units (Tables 2 to 7)2. Optional courses of major are 8 units (Tables 2 to 7)2. Thesis includes 20 units

After the successful completion of the educational stage, the research stage begins with the selection of the supervisor and preparing the research plan of the dissertation (Proposals) and ends with the compilation of the thesis and its defense.

Table 1Type: Specialized Subject: Computer Science Major: All Grade: M.Sc.

No. Course Unit Hours Prerequisite

1 Advanced Theory of Algorithm 4 64 -2 Advanced Theory of Computation 4 64 -3 Seminar 2 32 -Total 10 160

Passing these 10 units is obligatory for all M.Sc. students.

Table 2Type: Optional Subject: Computer Science Major: Algorithm, Logic and Computation Grade: M.sc and Ph.D.


1 Combinatorial Algorithms 4 64 -2 Parallel Algorithms 4 64 -3 Recursion Theory and Computability 4 64 Advanced Theory of Computation4 Computational Complexity 4 64 -5 Advanced Computational Complexity 4 64 Computational Complexity6 Approximation Algorithms 4 64 Advanced Theory of Algorithm7 Randomized Algorithms 4 64 Advanced Theory of Computation8 Computational Geometry 4 64 -9 Combinatorial Optimization 4 64 Advanced Theory of Algorithm10 DNA Computing 4 64 Advanced Theory of Algorithm11 Model Checking 4 64 -12 Logic Programming 4 64 -13 Modal Logic 4 64 -14 Category Theory 4 64 -15 Special Topics in Theory of Algorithm 4 64 Advanced Theory of Algorithm16 Special Topics in Theory of Computation 4 64 -Total 64 1024

M.Sc. (Ph.D.) students with major in Algorithm, Logic and Computation can pass at most 8 units (12 units) from the above table.

Table 3Type: Optional Subject: Computer Science Major: Artificial Intelligence Grade: M.sc and Ph.D.


1 Advanced Artificial Intelligence 4 64 -2 Machine Learning 4 64 -3 Image Processing 4 64 -4 Machine Vision 4 64 Image Processing5 Natural Language Processing 4 64 -6 Statistical Machine Learning 4 64 -7 Deep Learning 4 64 -8 Data Mining 4 64 -9 Speech Processing and Recognition 4 64 -10 Artificial Neural Networks 4 64 -11 Computational Neuroscience 4 64 -12 Robotics 4 64 -13 Special Topics in Artificial Intelligence 4 64 -Total 56 896

M.Sc. (Ph.D.) students with major in Artificial Intelligence can pass at most 8 units (12 units) from the above table.

Table 4Type: Optional Subject: Computer Science Major: Bioinformatics Grade: M.sc and Ph.D.


1 Bioinformatics 4 64 -2 Computational Systems Biology 4 64 -3 Macromolecules Structure Prediction and Modeling 4 64 Bioinformatics4 Protein Engineering and Proteomics 4 64 Bioinformatics5 High-throughput Biological Data 4 64 -6 Bioinformatics Databases 4 64 -7 Advanced Mathematics and Statistics for Bioinformatics 4 64 -8 Meta-heuristic Algorithms in Bioinformatics 4 64 Bioinformatics9 Machine Learning in Bioinformatics 4 64 Bioinformatics10 Computational Drug Design 4 64 -11 Modeling Metabolic Networks 4 64 -12 Biochemistry of Cell Signaling 4 64 -13 Special Topics in Bioinformatics 4 64 BioinformaticsTotal 52 832

M.Sc. (Ph.D.) students with major in Bioinformatics can pass at most 8 units (12 units) from the above table.

Table 5Type: Optional Subject: Computer Science Major: Data Science Grade: M.sc and Ph.D.


1 Machine Learning 4 64 -2 Statistical Machine Learning 4 64 -3 Mathematics of Learning 4 64 -4 Convex Optimization 4 64 Advanced Theory of Algorithm5 Data Mining 4 64 -6 Data Visualization 4 64 -7 Deep Learning 4 64 -8 Random Process 4 64 -9 Game Theory 4 64 -10 Big Data Modeling and Processing 4 64 Machine Learning11 Fuzzy Decision Making Systems 4 6412 Combinatroial Optimization 4 64 Advanced Theory of Algorithm13 Artificial Neural Networks 4 64 -14 Special Topics in Data Science 4 64 -Total 56 896

M.Sc. (Ph.D.) students with major in Data Science can pass at most 8 units (12 units) from the above table.

Table 6Type: Optional Subject: Computer Science Major: Computational Combinatorics Grade: M.sc and Ph.D.


1 Principle of Combinatorics 4 64 -2 Combinatorics on Words 4 64 -3 Enumerative Combinatorics 4 64 -4 Combinatorial Designs 4 64 -5 Probabilistic Method in Combinatorics 4 64 Principles of Combinatorics6 Theory of Cryptography 4 64 -7 Coding Theory 4 64 -8 Algebraic Graph Theory 4 64 -9 Game Theory 4 64 -10 Special Topics in Combinatorics 4 64 Principles of CombinatoricsTotal 40 640

M.Sc. (Ph.D.) students with major in Computational Combinatorics can pass at most 8 units (12 units) from the above table.

Table 7Type: Optional Subject: Computer Science Major: Formal Methods Grade: M.sc and Ph.D.

No. Course Unit Hours

Prerequisite

1 Algebraic Logic 4 64 -2 Computational Logic 4 64 -3 Automated Theorem Proving 4 64 -4 Logic and Formal Semantics 4 64 -5 Formal Verification 4 64 -6 Proof Theory 4 64 -7 Algebra and Coalgebra in Computer Sciences 4 64 -8 Computability and Arithmetic 4 64 Advanced Theory of Computation9 Special Topics in Formal Methods 4 64 -Total 36 576

M.Sc. (Ph.D.) students with major in Formal Methods can pass at most 8 units (12 units) from the above table.

Course Syllabus

Name: Advanced Theory of AlgorithmNumber of units: 4Unit type: 4 Theoretical Units, 0 Practical units Type of course: SpecializedPrerequisite courses: none

Course Objective:Study of Theoretical Aspects and Advanced Algorithms for Solving Hard Problems

Course Topics: 64 Theoretical hours, and 0 Practical hours

- Basic concepts of algorithms and complexity- Categorizing problems (various examples)- Deterministic approaches for solving hard problems (pseudo-polynomial algorithms,

parameterized complexity, lowering worse case) with various examples- Local search and its variations- Basic concepts of approximation algorithms, Categorizing problems from

approximability point of view, Approximation algorithms for hard problems (various examples)

- Basic concepts of randomized algorithms, Categorizing problems from randomization point of view, Randomized algorithms for hard problems (various examples)

- Recent approaches for solving hard problems (Heuristic algorithms, DNA computing)

Grading Policy:

ProjectFinal examMidterm ExamContinuous evaluation

20%Written Exam 40%Written Exam 20%20%Practical Exam- Practical Exam-

Materials and Resources:

1. J. Hromkovic, Algorithms for Hard Problems, Springer 2001. 2. T. H. Corman, C. E. Lisersion, and R.L. Rinest, Introduction to Algorithms, MIT Press,

2009.3. E. Tardos and J. Kleinberg, Algorithm Design, Pearson 2006.

Name: Advanced Theory of ComputationNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: SpecializedPrerequisite courses: none

Course Objective:Learning advanced issues in computability and gaining more expertise in logic and different models of computation.

Course Topics: 64 Theoretical hours, and 0 Practical hours- programs and computable functions- Macros, Primitive-Recursive functions, composition and recursion- PRC classes, Bounded Quantification, Primitive Recursive Propositions- Minimalization- Gödel numbers- Halting Problem- Recursively enumerable sets, Parameter theorem (s-m-n), Recursion Theorem, Rice and

Rice-Shapiro Theorem, Fixed-Point Theorem.- Computation on strings and numerical representation of them- Post-Turing programs- Grammar, Semi-Thue- Post Correspondence Problem- Quantification theory- The language of propositional logic, semantics, Herbrand’s theorem, - Gödel’s incompleteness theorems

Grading Policy:




1- M. D. Davis, R. Sigal, and E.J. Weynuker, Computability, Complexity and languages, Academic press, 1994.

2- H. Rogers, Theory of Recursive Functions and Effective Computability, MIT Press, 1987.

Name: Combinatorial AlgorithmsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

The aim of this course is to provide various methods to investigate combinatorial structures. In this course, the students will get acquainted with generation, ranking and unranking of combinatorial objects. Also, the applications of combinatorial algorithms are introduced.


- Introduction to object and combinatorial algorithms- Generation, ranking and unranking of combinatorial objects- Generating of subsets in lexicographical and Gray order- Generating of k-elements subsets in lexicographical and Gray order- Generating of permutations in lexicographical and Gray order- Integer partitions, Bell and Stirling numbers- Labeled trees and Catalan families- Backtracking algorithms for combinatorial objects- Heuristic search for combinatorial object generation

Grading Policy:

Project Final examMidterm ExamContinuous evaluation



1. D.L. Kreher and D.R. Stinson, Combinatorial Algorithms, generation, enumeration and search, CRC Press, New York, 2001.

2. D. E. Knuth, The Art of Computer Programming, vol. 4: Combinatorial Algorithm, Addison Wesley, New York, 2011.

3. H.S. Wilf, Combinatorial Algorithms: An updates, Academic Press, 1989.

Name: Parallel AlgorithmsNumber of units: 4Unit type: 4 Theoretical Units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Study of theoretical and practical aspects of parallel algorithms and their implementation technologies


- Parallel architectures (shared memory and interconnection network) and their computational models

- Expression and analysis of parallel algorithms- Basic parallel algorithms (broadcasting and summation)- Parallel algorithms for solving various problems (search, merge, sort, k-select matrix

multiplication, graph problems, etc.)- Bit-Complexity of parallel algorithms- Classification of problems from the perspective of parallel algorithms- Understanding the architecture of graphics cards, CUDA programming framework,

Practical implementation of parallel algorithms in CUDA

Grading Policy:ProjectFinal examMidterm ExamContinuous

evaluation20%Written Exam 40%Written Exam 20%20%

Practical Exam- Practical Exam-


1. S.G. Akl, The Design and Analysis of Parallel Algorithms, Prentice Hall, 1989.2. B. Parhami, Introduction to Parallel Processing: Algorithms and Architectures, Plenum

Press, 2000 3. F.T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays, Trees,

Hypercubes, Morgan Kaufmann, 1992. 4. J. Sanders and E. Kandrot, CUDA by Example, Addison-Wesley, 2010.

Name: Recursion Theory and ComputabilityNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Advanced Theory of Computation

Course Objective:This course is a continuation to “Advanced Theory of Computation” and includes more advanced topics from Recursion Theory.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Properties of functions and computable sets by various computational models (such as the

Turing, Davis and ...)- Partial recursive functions, r.e. sets and recursive sets (decidable sets)- The fixed-point theorem and its generalizations- Complete sets, Uniformity between sets, productive and creative sets- Rice-Shapiro's theorem, the Rice Theorem, the Recursion theorem and its equivalency to

the fixed-point theorem.- The relationship between logic and the theory of recursive functions- Kolmogorov algorithmic information theory and its connection to the theory of recursive

functions

Grading Policy:




1- S. B. Cooper, Computability Theory, Chapman and Hall, 2000.2- M. Machtey and P. Young, An introduction to the General Theory of Algorithms, North-

Holland Publisher Co., 1978.3- H. Rogers, Theory of Recursive Functions and Effective Computability, MIT Press,

1987.

Name: Computational ComplexityNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Studying some basic computational classes in the theory of computation and the relationship between them.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Preliminaries: Decision problem and languages, Turing machines- Time complexity for computation, space complexity for computation and speed-up

theorems for them- Complexity classes related to time and space and their comparison- Classes P, NP, PSPACE, CoNP, Lander Theorem- Alternative Turing Machine and Polynomial Hierarchy- Polynomial reduction and NP-Complete problems: Cook-Levin's Theorem- Statement of several NP-Complete issues- Non-deterministic space-Complexity classes, Savitch's theorem- PSPACE-Complete Problems, TQBF and 2-player games.

Grading Policy:




1- C. Papadimitriou, Computational Complexity, Addison-Wesley, 1994.2- M. Sipser, Introduction to the Theory of Computation, PWS Publishing Co., 2005.

Name: Advanced Computational ComplexityNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Computational Complexity

Course Objective:Studying some probabilistic and approximation computational classes

Course Topics: 64 Theoretical hours, and 0 Practical hours- Randomized algorithms and complexity classes PP, BPP, RP, CoRP and ZPP- The relationship between probabilistic classes and non-deterministic classes- Approximation algorithms, PTAS and FPTAS, APX Classes- Probabilistically Checkable Proofs (PCP) and the Hoastad Theorem, # P-Completeness- Parallel processing, circuits and the PRAM model, NC Class and P-Completeness- The complexity of communication

Grading Policy:




1- C. Papadimitriou, Computational Complexity, Addison-Wesley, 1994.2- M. Sipser, Introduction to the Theory of Computation, PWS Publishing Co., 2005.

Name: Approximation AlgorithmsNumber of units: 4Unit type: 4 Theoretical Units, 0 Practical units Type of course: OptionalPrerequisite courses: Advanced Theory of Algorithm

Course Objective:The approximation algorithms are based on method of choice for attacking intractable combinatorial optimization problems. By discussing some elegant general-purpose techniques which are developed for large classes of intractable problems, the students will know enough to be able to design approximation algorithms and use such results in several research areas.


- Basic concepts of approximation- Approximate algorithms- Evaluation of an approximate algorithm- Approximation algorithms for hard problems, For examples: Knapsack, vertex cover,

Traveling salesman problem (TSP), K-cut, set cover, bin packing, shortest superstring- Complexity of approximation algorithms- Categorization of problems from the perspective of approximation algorithms- LP-duality and some consequences- Inapproximability and its examples.





1. V. Vazirani. Approximation Algorithms. Springer-Verlag, Berlin, Germany, 2001. 2. J. Hromkovic, Algorithms for Hard Problems, Springer-Verlag Berlin Heidlberg, 2001.

Name: Randomized AlgorithmsNumber of units: 4Unit type: 4 Theoretical Units, 0 Practical units Type of course: OptionalPrerequisite courses: Advanced Theory of Algorithm

Course Objective:Study the theoretical and applied aspects of randomized algorithms


- Randomized algorithm design paradigms- Probability- Computational models and complexity classes of randomized algorithm- Random variables- Markov chains and random sampling- Probabilistic and conditional probability methods- Game theory, sampling and deviation- Algebraic methods- Randomized data structures- Applications of randomized algorithms





1. R. Motwani, P. Raghavan, Randomized Algorithms, Cambridge University Press, 1995. 2. J. Hromkovic, Algorithms for Hard Problems, Springer-Verlag Berlin Heidlberg, 2001.

Name: Computational GeometryNumber of units: 4Unit type: 4 Theoretical Units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Study theoretical and applied aspects of computational geometry


- Geometric objects such as dot, lines, semi-lines, polygons, and polyhedrals in geometric space

- Modeling and representing geometric objects- Intersection of lines and plans- Convex hulls- Veronoi diagram- Delaunay triangulation- Interval searches- Geometrical data structures for finding and searching geometric objects- Motion planning





1. M. de Berg, O. Cheong, M. Kreveld, and M. Overmars, Computational Geometry, Springer, 2010

Name: Combinatorial OptimizationNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Advanced Theory of Algorithm

Course Objective:The aim of this course is to introduce students to combinatorial optimization, the related concepts and methods. At the end of the course the students are ready to begin research in this field.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Problems and algorithms- Optimal trees and paths: minimum spanning trees, shortest paths - Maximum flow problems: network flow, application of max flow-min cut, minimum cuts

in undirected graphs- Minimum-cost flow problems, primal and dual minimum cost flow algorithms- Optimal matchings, maximum matching, minimum-weight perfect matchings, geometric

duality and the Goemans-Williamson algorithm- Integrality and polyhedral: convex hulls, polytopes, facets, integral polytopes, total

unimodularity, total dual integrality, cutting plans- The traveling salesman problem, heuristics for TSP, lower bounds, cutting plans, branch

and bound- Metroid: greedy algorithm, metroid intersection, application of weighted (weighted)

Metroid intersection- Complexity, problems in P, NP and NP-complete classes

Grading Policy:




1. W.J. Cook, W.H.Cunningham, W.R. Pulleyblank, and A. Schrijver, Combinatorial Optimization, John Wiley and Sons, 1998.

2. A. Schrijver, Combinatorial Optimization, Springer, 2003.3. B. Korte and J. Vygen, Combinatorial Optimization: Theory and applications, 3rd ed.,

Springer, 2006.

Name: DNA ComputingNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Advanced Theory of Algorithm

Course Objective:The aim of this course is to introduce students to the definition and history of molecular computing and its basic principles. At the end of this course, students will find how DNA computers can be used to calculate complex problems using biological molecules.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Introduction to molecular computing- Introduction to molecular biology- Molecular computing operations- Adelman experience- General molecular algorithms for solving NP problems- Molecular algorithms for solving Hamiltonian circuits and TSP- Molecular algorithm for solving shortest path problem- Computer memory modeling- Molecular algorithms for logical operations- Molecular dynamic programing algorithms

Grading Policy:




1. G. Paun, G. Kozenberg, and A. Salomaa, DNA Computing, New Computing Paradigms, Springer, 1998.

2. M. Amos, Theoretical and Experimental DNA Computation, Springer, Berlin, 2005.

Name: Model CheckingNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Some familiarity with formal methods for the correctness-checking of computer programs.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Transition systems,- Processor Algebra,- Concurrent systems- Linear-time system properties,- Temporal logic LTL- Correctness of linear-time properties- Introduction to the model checker SPIN

Grading Policy:




1- C. Baier and J. Katoen, Principles of Model Checking, MIT Press, 2008.2- E. M. Clarke, O. Grumberg, and D. A. Peled, Model Checking. MIT Press, 1999.

Name: Logic ProgrammingNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Some familiarity with logical programming languages like Prolog and Coq, and their applications in software foundations.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Declarative and Descriptive Programming Paradigm,- Logical programming language Coq, lists in Coq,- Designing Knowledge Base for an Intelligent Agent at Coq,- Backtracking and Unification- Logical inductive programming- Cognitive multi-agent programming- Logical multi-agent programming

Grading Policy:




1- M. Bramer, Logic Programming with Prolog, Springer, 2005.2- N. C. Rowe, Artificial Intelligence through Prolog, 1988.3- N. Lavrace and S. Dzeroski, Inductive Logic Programming, 1993.

Name: Modal LogicNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Familiarity with: relation structures, normal modal structures, Kripke models, decision problems in modal logics and definable structures in the language of the modal logic and its relation to the definitions in the first-order logic

Course Topics: 64 Theoretical hours, and 0 Practical hours- Modal languages,- syntax and meaning of the language;- Relational structures,- Bi-simulations and correspondences,- The Sahlqvist correspondence theory- Frames and their definitions,- Normal modal logics and complete theories- Duality,- General frames

Grading Policy:




1- M. de Rijke and Y. Venema, Modal Logic, Patrick Blackburn, Cambrisge University Press, 2002.

2- A. Chagrov and M. Zakharyaschev, Modal Logic, Clarendon Press, Oxford, 1997.

Name: Category TheoryNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Familiarity with the fundamental concepts of the Category Theory and the fundamental theorems of Category Theory.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Definition of the category, its properties and its introductory concepts- Structures on categories,- Functors - Categories derived from functors - Universal arrows- Adjoint relationship- Limit and Colimit- Indexed and inner categories- Basic Concepts of the Lambda Calculus

Grading Policy:




1- S. MacLane, Categories for the Working Mathematician, Vol. 5, Springer Science & Business Media, 1978.

2- S. Awodey, Category Theory, Oxford University Press, 2010.3- M. Kashivara and P. Schapira, Categories and Sheaves, Vol. 332, Springer Science &

Business Media, 2005.4- P.J. Freyd and A. Scedrov, Categories, Allegories, Vol. 39, Elsevier, 1990.

Name: Special Topics in Theory of AlgorithmNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Advanced Theory of Algorithm

Course Objective:

In this course advanced topics in Theory of Algorithm are introduced.


- The syllabus of this course is supposed to be prepared by the respective professor for proposed semester. The syllabus should be approved by the graduate council to be announced to the students prior to the registration for the semester.

Grading Policy:




Recent books and scientific articles relative to the topics of the syllabus.

Name: Special Topics in Theory of ComputationNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

In this course advanced topics in Theory of Computation are introduced.



Grading Policy:





Name: Advanced Artificial IntelligenceNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

This course introduces the advanced concepts of Artificial Intelligence (AI). After passing this course the students should be able to design an intelligent agent that can learn the properties of the environment by interaction with it, obtains the properties of the environment that cannot be derived directly by reasoning and plan for reaching to the goal.

Course Topics: 64 Theoretical hours, and 0 Practical hours Philosophical foundations of AI Intelligent agents and problems of AI Solving Problems by Searching Reinforcement Learning Advanced topics in learning Advanced topics in reasoning Advanced topics in planning

Grading Policy:




1. D. L. Poole and A. K. Mackworth, Artificial Intelligence: Foundations of Computational Agents, Cambridge University Press, 2010.

2. R. S. Sutton and A. G. Barto. Reinforcement Learning: An Introduction. Covers Markov decision processes and reinforcement learning, MIT Press, Second Edition, 2018.

Name: Machine LearningNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The course introduces concepts, approaches and basic algorithms in machine learning, with those machines can improve their performance based of experience. Providing the ability of using machine learning algorithms for solving different applications with different complexities and being familiar with pros and cons of these algorithms are other goals of this course.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Learning Concepts, introducing types of learning: Supervised, unsupervised and semi

supervised, reinforcement learning, introducing over fitting, classification, regression, clustering, prediction and presenting examples in machine learning applications

- Decision tree learning and pruning- Feed forward neural network, gradient descent, support vector machine and kernel-based

methods- Bayesian learning and statistical classification- K-means algorithm and Expectation Maximization- Performance measures for classification, regression and clustering- Combining learner models, reinforcement learning- Dimension reduction, semi supervised learning, active learning, online learning, deep

learning, multiclass classification

Grading Policy:




1- T. M. Mitchell, Machine Learning, McGraw-Hill Science, 1997.2- E. Alpaydin, Introduction to Machine Learning, The MIT Press, 3rd Edition, 2014.3- M. Mohri, A. Rostamizadeh, and A. Talwalkar, Foundations of Machine Learning, MIT

Press, 2012.4- C. M. Bishop, Pattern Recognition and Machine Learning, Springer, 2007.5- P. Flach, Machine Learning, The Art and Science of Algorithms that Make Sense of

Data, Cambridge University Press, 2012.

Name: Image ProcessingNumber of units: 4Unit type: 4 Theoretical Units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Nowadays image information is used in many organizations and locations. Digital image processing tools can be useful means for benefiting from this information. In this course, basic concepts in image processing are introduced. Introducing the concepts and applications of different methods for image enhancement, degradation modeling in images, compression, image coding, mathematical methods such as Fourier transforms, wavelet transform and morphological methods are the goals of this course.

Course Topics: 64 Theoretical hours and 0 Practical hours Introduction, Importance of image processing and its applications Introduction to various image types Image enhancement in spatial domain Spatial filtering and the variations Image enhancement id frequency domain 1-dimensional and 2-dimensional Fourier transform Image filtering in frequency domain Image compression Different redundancy in images Image coding methods and their properties Component of JPEG encoder Color image processing Morphology operator for binary and grey level images Morphology applications Image segmentation Convolutional neural networks and their applications





1. R.C. Gonzalez and R.E. Woods, Digital Image Processing, 4 th Edition, 2017.2. W. Pratt, Digital Image Processing, 2nd Edition, John Willy, 2007.

Name: Machine VisionNumber of units: 4Unit type: 4 Theoretical Units, 0 Practical units Type of course: OptionalPrerequisite courses: Image Processing

Course Objective:Study of vision and its computational modeling.


- Basic vision concepts in living organisms- Introduction to machine vision- Tools for machine vision systems- Image modification- Local representation of objects- 2D and 3D vision- Motion detection- Noise estimation and deletion- Linear and kernel operators





1. G. K. Davies, Machine Vision: Theory, Algorithms, Practicalities, Academic Press, 2005.2. R. Jain, R. Kasturi, and B. Schunck, Machine Vision, McGraw Hill, New York, 2003.

Name: Natural Language ProcessingNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The course provides a comprehensive overview over the theory and practice of natural language processing with main emphasis on current probabilistic, deep learning and machine learning techniques. The course includes an overview over typical NLP applications. In addition, the steps in a typical NLP system, like tokenization, morphological analysis, tagging, parsing, named entity recognition, relation extraction will be considered.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Introduction,- Tokenization,- Morphological analysis, - Sequence modeling & noisy channel model,- Statistical language modeling, smoothing techniques, perplexity, - Hidden Markov model, part-of-speech tagging,- Syntactic parsing, statistical and rule-based techniques, probabilistic context free grammar

(PCFG), Chomsky normal form, CYK algorithm,- Semantics parsing,- Natural language understanding,- Text-based information retrieval, text classification, - NLP applications (machine translation, question answering, dialog systems, text

summarization),- Word embedding,- RNN-based language modeling,- DNN-based techniques.

Grading Policy:




1. D. Jurafsky, J. H. Martin, Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistic, and Speech Recognition, Prentice Hall, 2009.

2. C. Manning and H. Schütze, Foundations of statistical natural language processing. MIT press, 1999.

3. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning, MIT Press, 2016.Name: Statistical Machine LearningNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:This course is an advanced course focusing on the intersection of Statistics and Machine Learning. This course presents an overview of advanced methods of statistical machine learning. Topics covered include both theoretical and practical aspects of advanced statistical learning. By the end of the course, the student must be able to formulate appropriate models for empirical data, justify the choice of a model to analyze data and explain the mathematical/statistical mechanisms of the machine learning algorithms.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Review of the decision theory,- Introduction: supervised and unsupervised learning, loss functions, train and test errors,

bias-variance tradeoff, model complexity and over-fitting,- Linear regression, generalized linear regression,- Linear classification, linear discriminant analysis, logistic regression,- Bayesian classifier and decision theory,- Parameter estimation techniques: maximum likelihood, MAP, Bayesian,- Unsupervised learning: Gaussian mixtures and the EM algorithm,- Hypothesis testing,- Theory of machine learning, - Graphical models: Hidden Markov model (HMM), conditional random field (CRF),

maximum entropy Markov model (MEMM),- Ensemble methods,- Variational Auto-encoders.

Grading Policy:

ProjectFinal examMidterm ExamContinuous evaluation20%Written Exam 40%Written Exam 20%20%



1. G. James, D. Witten, T. Hastie, and R. Tibshirani, An Introduction to Statistical Learning, with Applications in R. Springer, 2013.

2. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second edition, Springer, 2009.

3. B. Efron and T. Hastie, Computer Age Statistical Inference: Algorithms, Evidence and Data Science, Cambridge University Press, 2016.

Name: Deep LearningNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

This course introduces the concept of deep learning and the networks used for this aim. In addition it introduces the basic concepts and the ways of using deep networks in different applications.

Course Topics: 64 Theoretical hours, and 0 Practical hours Neurons and human brain, structure of the neurons, summary of natural neural networks,

concepts, definitions and constructive elements of neural networks Perceptron, single layer perceptron, classification by perceptron and its problem, linear

separable problems Feedforward multi-layer networks and backpropagation learning rule, classification and

regression via this network Improving back propagation networks and its variations, learning mechanism and power

of the network Regularization methods in deep learning Convolutional Neural Networks(CNN), deep learning by CNN Processor units, connections, associative patterns, feedforward associative networks,

single-layer recursive associative networks, training of recursive networks, deep recursive networks

Unsupervised representation learning Auto-encoders and representation learning via them Boltzmann machine, belief network, deep Boltzmann network, belief network Deep learning applications in machine vision, speech processing and natural language

processing

Grading Policy:




1. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning, MIT Press, 2016.2. J. Heaton, Artificial Intelligence for Humans, Volume 3: Deep Learning and Neural

Networks, Heaton, Research, Inc., 2015.3. J. Patterson and A. Gibson, Deep Learning: A Practitioner's Approach, O'Reilly Media,

2017.4. D. Yu and L. Deng, Automatic Speech Recognition: A Deep Learning Apprroach,

Springer, 2015.

Name: Data Mining Number of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The course introduces knowledge discovery process and its steps. The focus of this course is on the main step which is data mining. Students will be familiar to computational data mining methods and the way of using them in different applications. In addition by comparing these methods from time and space complexity viewpoints they will obtain the required capability to do research in this research field.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Introduction to knowledge discovery and the role of data mining in this process- Introduction to data preprocessing: data cleaning, integration, data reduction and

discretization- Introducing data warehouse and its architecture and implementation, online analytical

processing(OLAP)- Introducing data cube and data generalization- Introducing the concept of feature, dimension reduction methods, dimension reduction

based on statistical methods, feature ranking- Introducing basket analysis, Frequent Item Set, Frequent patterns- Introduction to classification methods and comparing their performance- Introduction to clustering methods and comparing their performance- Introduction to Curse of Dimensionality, feature extraction, feature selection and

dimension reduction methods

Grading Policy:




1. J. Han, M. Kamber, and J. Pei, Data Mining: Concepts and Techniques, 3rd Edition, Elsevier Inc., 2012.

2. C. C. Aggarwal, Data Mining: The Textbook, Springer, 2015.3. H. Witten, E. Frank, M. A. Hall, Data Mining: Practical Machine Learning Tools and

Techniques, 3rd Edition, Elsevier Inc., 2011.4. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning Data Mining,

Inference, and Prediction, 2nd edition, Springer, 2009.

Name: Speech Processing and RecognitionNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The course starts with the basics of human speech production and perception as well as theory of signal processing. The main part of the course covers how speech can be modeled for automatic speech recognition and the state-of-the-art techniques in automatic speech recognition. This course covers on other fields of speech processing such as speech synthesis, speech enhancement and speaker recognition as well. The objective of the course is thus not just to familiarize students with particular algorithms used in speech recognition, but rather use that as a basis to explore general text and speech and machine learning algorithms relevant to a variety of other areas in computer science.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Theory of speech production and speech perception,- Time-Frequency representations of speech signal,- short-time Fourier spectrum,- Speech recognition overview,- Large vocabulary continuous speech recognition, decoding,- HMMs, context-dependent models, acoustic modeling, language modeling, - Noise robustness, speaker adaptation, discreminative training,- DNN-based techniques in speech recognition,- Speech synthesis, dpeech enhancement, speaker recognition,- Speech processing applications.

Grading Policy:




1. D. Jurafsky and J. H. Martin, Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistic, and Speech Recognition, Prentice Hall, 2009.

2. D. Yu and L. Deng, Automatic Speech Recognition: A Deep Learning Approach, Springer, 2015.

Name: Artificial Neural NetworksNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

This course introduces the concept of neural networks and its applications. In addition it introduces the basic concepts and the ways of using neural networks for problem solving.

Course Topics: 64 Theoretical hours, and 0 Practical hours Introduction to natural neurons and human brain and its structure Definitions and constructive elements of neural networks McCulloch-Pitts Neurons Perceptron, single layer perceptron, classification by perceptron and its problem, linear

separable problems Hebb Net and adaline Autoassociative Net Feedforward multi-layer networks and backpropagation learning rule, classification and

regression via this network Improving back propagation networks and its variations, learning mechanism and power

of the network Kohonen Self organizing Maps, Learning Vector Quantization Hopfield Networks Adaptive Resonance Theory

Grading Policy:




1. L. Fausette, Fundamentals of Neural Networks, Architectures, Algorithms, and Application, Prentice Hall, 1944.

2. J. Hertz, A. Krogh, and R.G. Palmer, Introduction to the Theory of Neural Computation.3. H.R. Nielsen, Neurocomption, Addison-Wesley 1990.4. K. Simpson, Artificial Neural Systems, Foundations, Paradigms, Applications, and

Implementation, McGraw Hill, 1990.

Name: Computational NeuroscienceNumber of units: 4Unit type: 4 Theoretical Units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Study of brain structure, function, and its different regions and computational modeling of these areas


- Peripheral and central nerves system, different brain regions and their functions- Neurons and their variations, Synapse and its function- Learning in the brain- The primary visual cortex (retina, LGN, V1, V2)- Ventral (V2, V4, and IT) and Dorsal (V2, V3 and MT) pathways- PFC and its role in decision making- Brain mapping techniques- Modeling principles- Various models for spiking neurons, Spiking neural networks- Encoding and decoding methods of neuronal activities- Learning models and variations (unsupervised, supervised and reinforcement)- Polychrone groups- Introducing computational models, Convolutional spiking networks, Deep spiking

networks- Implementing spiking networks (event-driven or time based)





1. W. Gerstner, W. M. Kistler, R. Naud and L. Paninski, Neuronal Dynamics, Cambridge University press, 2014.

2. P. Dayan and L. E. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, MIT press, 2001.

Name: Robotics Number of units: 4Unit type: 4 Theoretical Units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The purpose of this course is to introduce basics of modeling, design, planning, and control of robot systems. In essence, the material treated in this course is a brief survey of relevant results from geometry, kinematics, statics, dynamics, and control. Also, the students will learn the basic methodologies and tools in robotics research and applications to move forward and experiment further in the robotics field.


- Introduction to Robotics- Homogenous coordinates and transform representations - Kinematic chain - Forward kinematics - Inverse kinematics: analytical methods - Differential kinematics: Jacobian computation, singular configurations - Configuration space operation - Mobile robots - Differential drive kinematics - Motion planning in robotics - Trajectory Generation-





1. R. G. Schilling, Fundamentals of Robotics, Prentice Hall, 1990.2. M. Spong and M. Vidyasagar, and S. Hutchinson, Robot Modeling and Control, John

Wiley & Sons, 2005.3. I. Craig, Introduction to Robotics: Mechanics & Control, Pearson 4nd Edition, 2017.4. H. Asada and J. Slotine, Robot Analysis and Control, John Wiley & Sons, 1992.

Name: Special Topics in Artificial IntelligenceNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

In this course advanced topics in Theory of Computation are introduced.



Grading Policy:





Name: BioinformaticsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

The aim of this course is to introduce students to the definition and history of bioinformatics and its basic principles. At the end of this course, students will find a general idea of the most important techniques that exist in various fields of bioinformatics. By studying new publications in this area, students will be familiar with state-of-the arts subjects.


- Introduction and History of Bioinformatics: A review of the collection and storage of biological sequences, biological databases, pairwise sequence alignment, multiple sequence alignment, looking for similar sequences (homology and BLAST), phylogenetic predictions

- Secondary biological databases- Knowledge based Databases- Protein-Protein Interaction Networks- Signaling networks- Cancer network - Regulatory networks- Study the structure of genome and the next generation sequencing of DNA.- Analysis of RNA-seq data- Microarray gene expression data- Introduction to biological networks- Introduction to systems biology- Introduction to synthetic biology- Introduction to brain Networks- Review the new Bioinformatics publications weekly

Grading Policy:Project Final examMidterm ExamContinuous




1. J. Pevsner, Bioinformatics and Functional Genomics. Wiley, 2015.2. P. Pevzner and R. Shamir, Bioinformatics for Biologists. Cambridge University Press,

2011.3. J.J. Ramsden, Bioinformatics: An Introduction. Springer Netherlands, 2012.

Name: Computational Systems BiologyNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

The aim of this course is to provide various computational and mathematical methods for modeling, simulating and analyzing biological networks. In recent years, many advances have been made in the collection of biological data, which led to development of new computational methods to analyze these data. Such discussions were usually dispersed in various biology courses. However, in recent years, there has been a new trend called computational systems biology, which in this course a wide range of biological systems is studied from a computational point of view.


- Systems in biology- Principles of reactive networks in biology- Modeling and simulation methods- Topological methods- Statistical Methods- Random methods- Linear and nonlinear differential equations- Dynamic systems- System analysis- Reduce complexity- Sustainability- Estimation and identification

Grading Policy:




1. B. Palsson, Systems Biology. Cambridge University Press, 2015.2. E. Klipp, et al., Systems Biology: A Textbook. Wiley, 2016.3. E. Klipp, et al., Systems Biology in Practice: Concepts, Implementation and Application.

Wiley, 2008.

Name: Macromolecules Structure Prediction and ModelingNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Bioinformatics

Course Objective:

The aim of this course is to introduce students to the structural principles of proteins and nucleic acids. It will also include information on the prediction of protein structures, nucleic acid structures, and the interaction between macromolecules.


- The structure of macromolecules- Classification of protein folding and relevant databases- Visualization of molecular structures- Analysis of biological sequences- Protein structure alignment- Protein secondary structure prediction- Comparison of protein structures- Force fields and minimization- Protein folding detection- Reverse protein folding- Docking- RNA secondary structure prediction

Grading Policy:




1. J. Gu and P.E. Bourne, Structural Bioinformatics. Wiley, 2011.2. C.I. Brändén and J. Tooze, Introduction to Protein Structure. Garland Pub., 1999.3. A.M. Lesk, Introduction to Protein Architecture: The Structural Biology of Proteins.

Oxford University Press, 2001.

Name: Protein Engineering and Proteomics Number of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Bioinformatics

Course Objective:

The aim of this course is to introduce students to the conventional methods of protein manipulation and the production of new proteins, as well as the importance of proteomics and its principles and methods.


- Introduction, Goals, Applications, and Types (with examples)- Strategies and criteria for selecting a mutation- Protein expression systems- De-Novo design and Rational design - Directed evolution - Methods of selecting and evaluating the desired mutation- Unnatural amino acids and their application in protein engineering- Proteomics and its goals- Proteome and its changes over time, conditions, diseases and etc- Types of proteomics: Structural, Functional, and Expressional- Protein separation techniques: Electrophoresis (One and Two Dimensions), HPLC,

Electrophoresis, and ...- Detection methods: proprietary and non-specific methods of gel staining in

electrophoresis- Protein identification methods and digestive methods for the production of peptides- Peptide sequencing using mass spectroscopy (MS) and analysis of findings using

databases and software

Grading Policy:Project Final examMidterm ExamContinuous




1. R.M. Twyman, Principles of Proteomics. Taylor & Francis Group, 2013.2. G. Drewes and M. Bantscheff, Chemical Proteomics: Methods and Protocols. Humana

Press, 2016.

Name: High-throughput Biological DataNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

The aim of this course is to increase skill of students for programming in bioinformatics and enhance their ability to analyze real biological data.


- R Programming language - R and BioConductor libraries- Analysis of gene expression data from microarrays- Mapping for Next-Generation Sequencing- Analysis of RNA Sequencing Data- Analysis of DNA methylation data- Analysis of histone modifications and transcription factors binding- Visualizing- Testing the significance of results in R- Incorrect inference in analysis

Grading Policy:




1. X. Wang, Next Generation Sequencing Data Analysis. Taylor & Francis, 2016.2. M.J. Crawley, The R Book. Wiley, 2012.3. R.C. Team, An Introduction to R. Samurai Media Limited, 2015.

Name: Bioinformatics DatabasesNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

After Human genome sequencing and increasing the interest in analyzing proteins and molecular structures, biological databases have been developed. In this course, a wide range of biological databases including genome databases such as GenBank and Ensemble, as well as protein databases like PDB and SWISS-PROT will be introduced and the students will be learned how to use these databases. Some tools for accessing databases are covered in this course. Specialized databases and their applications are also discussed.


- An introduction to the biological databases- Sequence and Structure Databases such as Jasper, String, Uniprot, PDB, EMBL, NCBI

and ...- Data access and Data retrieval in Bioinformatics databases- Design and develop a bioinformatics database- Bioinformatics Databases: Web services- Standards for data storage and data exchange between bioinformatics databases - Hospital information system- Doing a practical project

Grading Policy:




1. J. Chen and A.S. Sidhu, Biological Database Modeling. Artech House, 2008.2. H. Garcia-Molina, J.D. Ullman, and J. Widom, Database Systems: The Complete Book.

Pearson Education Limited, 2013.3. S.I. Letovsky, Bioinformatics: Databases and Systems. Springer US, 2006.4. J.T.L. Wang and K.G. Herbert, Bioinformatics Database Systems. Taylor & Francis,

2016.

Name: Advanced Mathematics and Statistics for BioinformaticsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

The aim of this course is to provide the necessary preliminaries for increasing the mathematical knowledge of students.


- The estimation methods- Test of statistical hypothesis- Calculation and modification of all types of meaningful data values- Confidence intervals- Bayesian statistics and inferences- Bayesian networks- Bayesian Networks Learning Softwares- Graph theory and biological networks modeling- Statistical graphical models- Network analysis software such as Cytoscape- Differential equations, dynamical systems, and their application in systems biology- An Introduction to Linear Algebra- Software for Differential Equation analysis and ODE

Grading Policy:




1. E.K. Yeargers, J.V. Herod, and R.W. Shonkweiler, An Introduction to the Mathematics of Biology: with Computer Algebra Models. Birkhäuser, Boston, 2013.

2. J. Fowler, L. Cohen, and P. Jarvis, Practical Statistics for Field Biology. Wiley, 2013.3. M. He and S. Petoukhov, Mathematics of Bioinformatics: Theory, Methods and

Applications. Wiley, 2011.

Name: Meta-heuristic Algorithms in BioinformaticsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Bioinformatics

Course Objective:

The aim of this course is to introduce students to the meta-heuristic methods in bioinformatics applications related to optimization.


- The combinatorial optimization algorithms- Genetic algorithms and their applications in bioinformatics- Simulated Annealing Algorithms- Ant colony algorithms

Grading Policy:




1. P. Baldi, et al., Bioinformatics: The Machine Learning Approach. A Bradford Book, 2001.

2. L. Geris and D. Gomez-Cabrero, Uncertainty in Biology: A Computational Modeling Approach. Springer International Publishing, 2015.

Name: Machine Learning in BioinformaticsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Bioinformatics

Course Objective:

The aim of this course is to introduce students to the machine learning algorithms in bioinformatics including supervised, unsupervised, semi-supervised and reinforcement methods.


- An introduction to machine learning algorithms- Probabilistic modeling and inference- Unsupervised learning methods- Clustering in gene expression data- Supervised learning methods- Classification in Bioinformatics- An introduction to neural networks- Applications of neural networks in DNA, RNA and protein problems- An introduction to hidden markov models (HMMs)- Applications of HMMs in DNA, RNA and protein problems- Probabilistic models of evolution: phylogenetic tree

Grading Policy:




1. P. Baldi, et al., Bioinformatics: The Machine Learning Approach. A Bradford Book, 2001.

2. A. Moses, Statistical Modeling and Machine Learning for Molecular Biology. CRC Press, 2017.

3. Z.R. Yang, Machine Learning Approaches to Bioinformatics. World Scientific, 2010.4. Y. Zhang and J.C. Rajapakse, Machine Learning in Bioinformatics. Wiley, 2009.

Name: Computational Drug DesignNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

The aim of this course is to introduce students to the drug design using a variety of computational methods.


- An introduction to the drug and its receptor- History and the discovery of new drugs- The drug development process - Great challenges in the drug discovery process- Drug design process- Ligand-based drug design- Structure-based drug design- Computational tools and techniques: (homology modeling, molecular mechanics, protein

folding, docking, pharmacokinetic models, QSAR, 3D-QSAR, cheminformatics)- ADMET- Virtual screening- Fragment-based drug design

Grading Policy:




1. D.C. Young, Computational Drug Design: A Guide for Computational and Medicinal Chemists. Wiley, 2009.

2. P. Bultinck, et al., Computational Medicinal Chemistry for Drug Discovery. Taylor & Francis, 2003.

3. T. Mavromoustakos and T.F. Kellici, Rational Drug Design: Methods and Protocols. Springer, New York, 2018.

4. L.W. Tari, Structure-Based Drug Discovery. Humana Press, 2012.

Name: Modeling Metabolic NetworksNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

The aim of this course is to introduce students to different methods of modeling metabolic networks and its practical applications in biology and biotechnology.


- A review of network biology- An introduction to the linear algebra and convex analysis- An introduction to the basic concepts of metabolism (metabolite, reaction, metabolic flux,

reversibility of reactions, ...)- Reconstruction of metabolic networks- Constraint-based modeling in metabolic networks- Flux balance analysis- Flux coupling analysis and flux correlation analysis- Flux variability analysis and alternative optima analysis- Study the effects of mutations (MOMA and ROOM analyzes)- Strain design- Path analysis in metabolic networks- Modeling the regulation of metabolic networks- Metabolic control analysis- Metabolic flux Analysis- Principles of Metabolic Engineering

Grading Policy:




1. B.Ø. Palsson, Systems Biology: Properties of Reconstructed Networks. Cambridge University Press, 2006.

Name: Biochemistry of Cell SignalingNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

The aim of this course is to describe the structural and biochemical properties of cellular signals and their regulations. It also describes how to transfer signals in the cell, signaling pathways and the interactions among them.


- Cellular signaling mechanisms- Receptors involved in cellular signaling- Intracellular receptors (structure / function, coactivator / corepressor and JAK/STAT).- Membrane receptors- G-protein-coupled receptor- Receptors with tyrosine-specific protein kinase activity- Ligand gated ion channel receptor- Second messengers- cAMP- Calcium- Lipophilic- Reactive oxygen species, reactive nitrogen species- Ser/Thr-specific protein kinases and protein phosphatase signaling- Cellular signaling with Ras proteins- Cellular signaling in disease and health

Grading Policy:




1. B.D. Gomperts, M. Kramer, and P.E.R. Tatham, Signal Transduction. Elsevier Science, 2002.

2. G. Krauss, Biochemistry of Signal Transduction and Regulation. Wiley, 2006.

Name: Advanced Topics in BioinformaticsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Bioinformatics

Course Objective:

In this course advanced topics in Bioinformatics are introduced.



Grading Policy:





Name: Mathematics of LearningNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:This course aims to explain the mathematics on which machine learning depends: linear algebra, optimization probability and statistics. It helps students to organize central methods and idea of machine learning and to see how language of mathematics gives expression to those methods and ideas.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Linear Algebra, orthogonal matrices and subspaces, symmetric positive definite matrices,

singular value decomposition, principal components, norms of vectors and function and matrices, factoring matrices and tensors,

- Computations with large matrices, numerical linear algebra, least squares,- Low rank and compressed sensing,- Fourier transform: discrete and continuous,- Clustering by spectral methods,- Probability and Statistics, probability distributions, inequalities of statistics, covariance

matrices and joint probabilities, multivariate Gaussian, Markov chains,- Optimization, convexity and Newton’s methods, Lagrange multipliers, Linear Programming,

stochastic gradient decent.

Grading Policy:




1. G. Strang, Linear Algebra and Learning from Data, Cambridge University Press, 20192. J. Korevaar, Mathematical Methods: Linear Algebra, Normed Spaces, Distributions,

Integration, Dover Publications, 2008.3. V. Vapnik, Statistical Learning Theory, John Wiley & Sons, 1998.

Name: Convex OptimizationNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Advanced Theory of Algorithm

Course Objective:The aim of this course is to help students develop a working knowledge of convex optimization, i.e., to develop the skills and background needed to recognize, formulate, and solve convex optimization problems.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Introduction to optimization,- Convex sets, separating and supporting hyper plane, extended inequalities, dual cones, - Convex functions, conjugate functions, quasi-convex functions, - Convex optimization problems, quadratic programming, geometric programming, - Duality, Lagrange duality, optimality conditions, sensitivity analysis, - Approximation and regression, Norm approximation, least-norm problems, function fitting, - Statistical estimation, non-/parametric distribution estimation, - Geometric problems, projection on a set, distance between sets, centering, classification,- Unconstrained minimization,- Equality constrained minimization,- Interior-point methods.

Grading Policy:




1. D. P. Bertsekas, Convex Optimization Theory, Athena Scientific, 2009.2. D. P. Bertsekas, Nonlinear Programming, 3rd Edition, Athena Scientific, 2016.3. D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 4th Edition, Springer,

2015.

Name: Data VisualizationNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

This course introduces the key rules and basis for data visualization and shows the learners how data visualization can be useful in understanding the complex data. The aim of this course is improving the capabilities of learners for investigation in this research field.

Course Topics: 64 Theoretical hours, and 0 Practical hours Introducing data visualization and its importance Types of data and datasets, data abstraction methods, task abstraction methods Symbols and channels, data coding by symbols and channels, channel performance

measures, accuracy, discriminability, separability, popout, integrality Rules should be considered in data visualization Validation and its four levels Design of data table, spatial data, network data and tree based structures layout Color mapping and non-spatial channels in visual coding, view manipulation methods,

complex data visualization Item reduction and feature reduction for handling the complexities of visualization Data inserting methods on a selected view Introducing data visualization systems and their capabilities like Scagnostics, VisDB,

PivotGraph, InterRing, Constellation and Hierarchical Clustering Explorer

Grading Policy:




1. T. Munzner, Visualization Analysis and Design, CRC Press, 2014.2. G. Dzemyda, O. Kurasova, and J. Zilinskas, Multidimensional Data Visualization:

Methods and Applications, Springer, 2013.3. S. Murray, Interactive Data Visualization for the Web, O'Reilly Media, 2013.4. I. Meirelles, Design for Information: An Introduction to the Histories, Theories, and Best

Practices Behind Effective Information Visualizations, Rockport Publishers, 2013.

Name: Random ProcessNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:This foundational course will introduce students to basics of probability theory, random variables, and random sequences so that they have needed skills and background to formulate and solve problems from the random process perspective.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Probability Theory: axioms, continuity of probability, independence, conditional

probability,- Random variables: distribution, transformation, expectation, moment generating function,

characteristic function,- Random vectors: joint distribution, conditional distribution, expectation, Gaussian random

vectors,- Convergence of random sequences: Borel-Cantelli Lemma, laws of large numbers, central

limit theorem, Chernoff bound,- Discrete time random processes: ergodicity, strong ergodic theorem, definition, stationarity,

correlation functions in linear systems, power spectral density,- Structured random processes: Bernoulli processes, independent increment processes,

discrete time Markov chains, recurrence analysis, Foster's theorem, reversible Markov chains, the Poisson process.

Grading Policy:




1. R. Gallager, Stochastic processes: theory for applications. Cambridge University Press, 2013.

2. A. Papoulis and S.U. Pillai. Probability, random variables, and stochastic processes. Tata McGraw-Hill Education, 2002.

3. K. Hisashi, B. L. Mark, and W. Turin, Probability, Random processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance, Cambridge University Press, 2011.

Name: Game TheoryNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The aim of this course is to provide an introduction to the basic techniques of game theory and to illustrate the range of its applications in various areas. After passing the course the student should be familiar with basic concepts, models and theorems in the game theory.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Review of the decision theory,- Strategic games and Nash equilibrium, mixed equilibrium,- Extensive games with complete information,- Extensive games with incomplete information,- Bayesian Games,- Repeated Games,- Auction,- Mechanism design,- Bargaining.

Grading Policy:




1. R.B. Myerson, Game theory. Harvard university press, 2013.2. N. Nisan, Algorithmic Game Theory, Cambridge University Press, 2007.3. M.J. Osborne and A. Rubinstein. A course in game theory. MIT press, 1994.

Name: Big Data Modeling and ProcessingNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Machine Learning

Course Objective:This foundational course will introduce students to the concepts of large data and how to manage and analyze them, and provide the needed knowledge and insight to enter advanced topics in this field.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Introduction to big data, three key sources of its production,- Six attributes of big data (volume, speed, diversity, accuracy, capacity and value),- Big data analysis and reporting,- Describing programming models for large scale analysis of scalable data, introduction to big

data processing steps,- Methods for accessing and manipulating data stream, - Introducing Hadoop, YARN, MapReduce,- Retrieve, integrate and analyze big data,- Analysis of graph-based big data,- Classification, regression, clustering and analysis of big data coherence,- Implementing a sample of data management system.Grading Policy:




1. R. Buyya, R. N. Calheiros, and A. Vahid Dastjerdi, Big Data. Principles and Paradigms, Morgan Kaufmann, 2016.

2. F. Corea, Big Data Analytics: A Management Perspective, Springer, 2016.3. I. Foster, R. Ghani, R. S. Jarmin, F. Kreuter, and J. Lane, Big Data and Social Science: A

Practical Guide to Methods and Tools, Chapman & Hall/CRC, 2017.

Name: Fuzzy Decision Making Systems Number of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:In many application the best decision should be made in the presence of inaccurate and approximated information. The aim of this course is being familiar by the mathematics that be used in such situations.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Fuzzy sets and the operation, fuzzy numbers and their computation, fuzzy graph and fuzzy

logic- Linear fuzzy planning methods- Decision making by fuzzy parameters- Applications: transport, production planning, expert systems

Grading Policy:




1. H.j. Zimmermann, Fuzzy Sets Theory and Its Application, Kluwer Academic Pub., 1996.2. Y.J. Lai, and C.L. Hwang, Fuzzy Mathematical Programming: Methods and Applications,

Springer, 1992.3. K. P. Yoon and C.L. Hwang, Multiple Attribute Decision Making: An Introduction, Sage

Publications Inc., 1995.4. J. Figueira, S. Greco, and M. Ehrgott, Multiple Criteria Decision Analysis: State of the Art

Surveys, Springer, 2005.

Name: Special Topics in Data ScienceNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

In this course advanced topics in Data Science are introduced.



Grading Policy:





Name: Principle of CombinatoricsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The aim of this course is to introduce graduate students with some concepts and techniques of combinatorics. At the end of the course, they will be able to apply these techniques to research problems in theoretical computer science and elsewhere.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Recurrence Problems, Sums, Integer functions- Generating functions, Asymptotic relations- Problems from enumerative cominatorics, PIE- Special numbers: Stirling and Bell numbers, Eulerian and Bernoulli numbers- Harmonic numbers, Fibonacci numbers- Continuants and continued fractions- Ramsey and Turan theorems, Lovasz local lemma, some applications- Extremal set theory and Dilworth Theorem- System of distinct representatives and Hall theorem- Integer partitions, Ferrers Board and Young tableaux- (0,1)-matrices, orthogonal Latin squares- Hadamard matrices and Reed-Muller codes- Association schemes, Delsarte inequalitis, polynomial schemes

Grading Policy:




1- R.L.Graham, D.E. Knuth and O. Patashnik, Concrete Mathematics, 2nd ed., Addison Wesley, 1994.

2- J. Van Lint and R.M.Wilson, A Course in Combinatorics, 2nd ed., Cambridge University Press, 1992.

3- T. Mansour and M. Schork, Commutation Relations, Normal Ordering and Stirling Numbers, CRC Press, 2016.

4- H. J. Ryser, Combinatorial Mathematic, The Mathematical Association of America, 1993.

Name: Combinatorics on WordsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The aim of this course is to introduce students to combinatorics on words which is a relatively new topic in combinatorics and has many connections with automata theory, languages, number theory, algorithmics and so on. The students learn several concepts and techniques which are helpful in the research in connection with different fields.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Introduction of monoid, submonoid, morphism, free monoid, word- conjugate words, primitive word, period of a word, border of a word- prolongable morphism, (purely) morphic words, complexity function of a word and its

properties, dependency of words, code, Fine-Wilf theorem- Christoffel words and morphisms, Lyndon words, standard factorization- Christoffel words and continued fractions, palindrome words and palindrome closure- Burrows-Wheeler transform, characterizations of Christoffel words- Cycle lemma and consequences, Dyck words and language, Dyck factorization - Thue-Morse morphism and word, Tarry-Escott problem, connection with magic squares- Automatic words and some examples, Algebraic characterization (Christol’s theorem)- Combinatorics of the Thue-Morse word, connection with the Tower of Hanoi’s problem- Square-free and overlap-free words, (counting) squares in words- Some other factorizations of words: Ziv-Lempel, Crochemore, Viennot, grammer-based- Repetitions and patterns in words,- Text algorithms: Finding border of a word, KMP algorithm

Grading Policy:




1. J. Berstel, A. Lauve, Ch. Reutenauer, and F. V. Saliola, Combinatorics on Words, AMS, CRM vol 27, 2008.

2. M. Lothaire, Applied Combinatorics on Words, Cambridge University Press, London, 2005.

3. V. Berthe and M. Rigo, Combinatorics, Automata and Number Theory, Cambridge University Press, London, 2010.

4. M. Crochemore and W. Rytter, Jewels of Stringology, Word Scinetific, 2002.

Name: Enumerative CombinatoricsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The aim of this course is to introduce students to problems and techniques of enumerative combinatorics and especially with its fundamental tool, i.e. generating functions and their connections with algebra and complex analysis.


- Geometric representation of permutations, Increasing (binary) and min-max trees- Permutations of multisets, Partition identities, The twelvefold way- Admissible (unlabeled and labelled) combinatorial structures, ordinary and exponential

Generating Functions (GFs), labelled products and marking points- Formal and analytic theory of power series, rational, algebraic, D-finite, noncommutative,

Bivariate and multivariate GFs,The Sieve method, PIE, Ferrers boards, unimodal sequences- Posets: lattices, distributive lattices, Eulerian and binomial posets- Incidence algebras and Mobius inversion, Zeta polynomials,- Polynomials and quasipolynomials, Linear homogenous Diophantine equations- Counting magic squares, The transfer matrix method- Trees and GFs: Lagrange inversion, Lagrange Burmann formula, oriented trees and the

matrix-tree theorem- Symmetric Functions (SFs): Monomial, Elementary, Complete homogeneous, power sum

SFs, Schur functions, The RSK algorithm and its dual, Plane partitions- Complex analysis: Implicit function Theorem, Residue Theorem, Cauchy’s formula- Analyticity and singularities, meromorphic functions and poles, dominant singularities- Saddle point (Hayman), Circle (Darboux) and Transfer (Odlyzko-Flajolet) methods- Random variables and random structures

Grading Policy:




1. P.J. Cameron, Notes on Counting, Cambridge University Press, 2017.2. R. P. Stanley, Enumerative Combinatorics, 2nd ed., Cambridge University Press, 1997.3. Ph. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press,

2007.

4. H.S. Wilf, Genratingfunctionology, 2nd ed., Academic Press, 1994.

Name: Combinatorial DesignsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The aim of this course is to introduce students to several kinds of combinatorial designs. At the end of this course, students will know about the connections between different combinatorial designs and their applications in research problems of various kinds.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Introduction of BIBD and PBD, Fisher’s inequality- Finite fields and related computations - Symmetric BIBD, The BCR theorem- Difference sets and automorphisms, The multiplier theorem- Hadamard matrices and some constructions- orthogonal and self-orthogonal Latic squares, Euler’s conjecture and its end- Orthogonal arrays and codes- Transversal designs and Wilson’s Theorem- Steiner and Kirkman Triple systems, t-wise balanced designs- Association schemes and related concepts

Grading Policy:




1. D. R. Stinson, Combinatorial Designs: Constructions and Analysis, Springer, 2004.2. I. Anderson, Combinatorial Designs and Tournaments, Oxford University Press, 1996. 3. I. Anderson, Combinatorial Designs: Construction Methods, John Wiley and Sons, 1990.

Name: Probabilistic Method in Combinatorics Number of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Principles of Combinatorics

Course Objective:The aim of this course is to introduce students to the probabilistic method in combinatorics and to make him\her able to use this technique in related research problems.


- The basic method, Ramsey numbers, Dominating sets in graphs, Hypergraph 2-coloring, Set pairs theorem. Linearity of expectation, Sum-free subsets, Hamiltonian paths in tournaments.

- Alterations, Cliques in random graphs. Alterations: Graphs with high girth and high chromatic number, bounding of large deviations and consistent arcs in tournaments.

- The second moment method, Turan's proof of the Hardy Ramanujan theorem, distinct sums, random graphs and threshold functions.

- The Local Lemma: the general lemma and its symmetric version, Straus' problem, directed cycles.

- Correlation Inequalities: the four functions theorem and its applications, the FKG Inequality, The Harris-Kleitman Theorem, correlation between properties of random graphs

- Martingales: The edge exposure and the vertex exposure martingales, Azuma's Inequality. Chromatic number of random graphs.

- Poisson approximation: The Janson Inequalities and their application for constructing Ramsey type graphs and for estimating the chromatic number of G(n,1/2).

- Geometry: the VC dimension of a range space and its applications.

Grading Policy:




1. N. Alon and J. H. Spencer, The Probabilistic Method, Fourth Edition, Wiley, 2016.2. B. Bollobas, Random Graphs, Second Edition, Cambridge University Press, 2001.3. S. Janson, T, Luczak and A. Rucinski, Random Graphs, Wiley, 2000.

Name: Theory of CryptographyNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The aim of this course is to introduce students to the classical and advanced cryptography systems and analysis of different cryptography systems and related theoretical concepts. At the end of the course the students are ready to begin research in this field.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Classical cryptography: the shift cipher, the substitution cipher, the affine cipher, …,

cryptanalysis- Shannon’s theory: elementary probability theory, perfect secrecy, entropy, Huffman

encodings- Advance encryption standard : The data encryption standard (DES), the advance encryption

standard (AES), analyses of DES and AES - Cryptographic hash function- Public key cryptography, RSA, related number theoretical concepts, implementing RSA,

Robin cryptosystem, semantic security of RSA- Discrete logarithm problem: The Elgamal cryptosystem, algorithms for discrete logarithm

problems, related concepts: finite fields, elliptic curves- Signature schemes, provably secure signature schemes- Key distribution, Diffie-Hellman key predistribution, key distribution patterns- Secret sharing scheme, Shamir threshold scheme, access structure and general secret

sharing

Grading Policy:




1. D. B. Stinson. Cryptography: Theory and Practice, Third Edition, Sringer, 2005.2. J. Katz, Introduction to Modern Cryptography: Principles and Protocols, Chapman &

Hall/CRC , 2007.

Name: Coding TheoryNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The aim of this course is to introduce students to coding theory and its main problems and techniques. At the end of this course, students will know about the connections between coding theory and related combinatorial objects such as combinatorial designs.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Finite fields and their structure, minimal polynomials- Linear codes, Generator and pariry check matrices- Equivalence of codes, Encoding and decoding of linear codes- The main problem of coding theory, sphere covering and Gilber-Warshamov bounds- Perfect codes, Hammin, Golay and MDS codes- Singleton, Plotkin, Griesmer and LP bound- Nonlinear codes, Hadamard matrix codes, Preparata and Kerdock codes- Nordstorm-Robinson code, Reed-Muller codes, subfield codes- Cyclic codes, generator polynomials, generator and parity-check matrices- BCH, Reed-Solomon, Quadratic-residue codes- Generalized Reed-Solomon, Alternant, Goppa codes- Weight distributions, MacWilliams equations, - Pless power moments, Gleason polynomials- Designs and codes, The Assmus-Mattson Theorem, Symmetry codes-

Grading Policy:




1. S. Ling and Ch. Xing, Coding Theory; A First Course, Cambridge University Press, 2004.

2. V. Pless, Introduction to the Theory of Error Correcting Codes, 2nd ed., John Wiley and Sons, 1989.

Name: Algebraic Graph Theory Number of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:The aim of this course is to introduce students to the theory concepts and techniques and problems of algebraic graph theory, particularly applications of linear algebra in the theory of graphs.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Graphs: subgraphs, automorphisms, homomorphisms, circulant graphs, Johnson graphs,

line graphs.- Matrix Theory: the adjacency matrix, the incidence matrix, spectra of graphs, The Perron-

Frobenius Theorem, the rank of a symmetric matrix and the rank of a graph, computing spectra of special families of graphs.

- Linear Algebra and Graph Theory: regular graphs and line graphs, cycles and cuts, spanning trees and associated structures, the matrix-tree theorem, determinant expansion.

- Interlacing Theorem: equitable partitions, spectra of Kneser graphs, bipartite subgraphs. - Laplacian of a Graph: the laplacian matrix, representations, energies and eigeivalues,

connectivity- Symmetry and Regularity: vertex-transitive graphs, edge-transitive graphs, edge

connectivity, vertex connectivity, matching, symmetric graphs, distance-transitive graphs, intersection arrays, feasibility of intersection arrays.

Grading Policy:




1. C. Godsil and G. Royle, Algebraic Graph Theory, Springer-Verlag, New York, 2001.2. N. Biggs, Algebraic Graph Theory, Cambridge University Press, 1993.3. D. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs, Johann Ambrosius Barth, 1995.4. R. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge University Press,

1991.

Name: Special Topics in CombinatoricsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Principle of Combinatorics

Course Objective:

In this course advanced topics in Combinatorics are introduced.



Grading Policy:





Name: Algebraic LogicNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Basic familiarity with the classical and non-classical logics, Algebraic semantics for variety of logics, criterions for classification of several logics and algebrization for classical, intuitionistic and modal logics.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Basics from universal algebra: definition of algebra, term algebra, free algebra, sub-

algebra, homeomorphism, congruence, quotient algebra, variety and quasi variety, distributive lattices, complete lattices, filters, ideals, duality of distributive lattices.

- Propositional languages, consequence operations, propositional logics, logic as a consequence system, matrix models, Leibniz model, operations on matrix models, Leibniz congruence, reduced matices.

- Algebrization of propositional logics: equivalent sentences, Suzko operation, free matrices, injectivity of Lebniz operations, weak surjectivity of structural consequence, algebrizable logic, Blok and Pigozzi’s algebrization.

- Fregean logics: Fregean axioms, Fregean logic, Fregean quasi variety, Hilbertian quasi variety.

- Algebrization of important logics: intuitionistic logic, classical logic, linear logic and modal logic.

Grading Policy:




1- J. Czelakowski, Protoalgebraic Logics, Springer, 2001.2- R. Jansana, A General Algebraic Semantics for Sentential Logics, 2nd Edition, Iosep

Maria Font and Lecture Notes in Logic, Vol. 7, Springer-Verlag, 2009.3- R. Wojcicki, Theory of Logical Calculi, Basic Theory of Consequence Operations,

Springer, 1988.4- A. Koslow, A Structurialist Theory of Logic, Combridge University Press, 1992.

Name: Computational LogicNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Advanced Theory of Computation

Course Objective:Familiarity with the computational logic methodology and its basic concepts.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Topics on theoretical and practical aspects- Automated Theorem Proving, including the basic methodology of computational logic,

automated proof for propositional and first order logic- Artificial intelligence in logic- Programming logic, linear logic- Computational complexity theorem

Grading Policy:




1- A. C. Kakas, Computational Logic: Logic Programming and beyond, Springer, 2002.2- L. Sterling and E. Shapiro, The Art of Prolog: Logic Programming, MIT Press, 199.3- D. M. Gabbay, T. S. E. Mabaum and S. Abramsky, Handbook of Logic in Computer

Science, Oxford University Press.

Name: Automated Theorem ProvingNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Familiarity with the basic concepts of automated theorem proving and its applications.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Mathematical Preliminaries - Propositional logic- First order logic- Cut elimination theorem and its applications- Gentzen Sharpened Hauptsatz- Herbrand Theorem- Analysis in propositional logic and first order- Analysis of SLD and Prolog- Many-sorted First-Order Logic

Grading Policy:


0%Written Exam 50%Written Exam 40%10%Practical Exam -Practical Exam -


1- J. H. Gallier, Logic for Computer Science, Foundation of Automatic Theorem Proving, Harper & Row, 2003.

2- F. Pfenning, Automated Theorem Proving, Lecture notes, March 2004.

Name: Logic and Formal SemanticsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Familiarity with the formal (syntactical or logical) methods for the study of the semantics of the programming languages.

Course Topics: 64 Theoretical hours, and 0 Practical hours- The formal semantics of programming languages- Denotational Semantics- Lambda calculus- Recursive semantics and fixed-point - Domain Theory- Operational Semantics- Axiomatic semantics

Grading Policy:




1- G. Winskel, the Formal Semantics of Programming Languages, 1993.2- C. Gunter, Semantics of Programming Languages, MIT Press, 1992.

Name: Formal VerificationNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Familiarity with the formal (syntactical or logical) methods for the correctness examination of software and hardware systems.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Hoar Logic- First order logic- Dynamic logic- The formal description of the Java programming language- Key Tool

Grading Policy:




1- J. Laski, and W. Stanley, Software Verification and Analysis, Springer, 2009. 2- B. Beckert, Verification of Object Oriented Software, the KEY Approach, Springer,

2007.

Name: Proof TheoryNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Studying the essential properties of proofs as mathematical objects.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Backgrounds from logic: Classical and intuitionistic logic devices- Natural deduction system and Hilbert-style systems- Sequent Calculus- Cut-elimination and its applications: Provisional and first order arithmetic- Bounds and permutations- Normalization for natural deduction

Grading Policy:




1- A. S. Troelstra and H. Schwichtenberg, Basic Proof Theory, Cambridge University Press, 1996.

2- G. Takeuti, Proof Theory: Second Edition, North-Holland, 1987.

Name: Algebra and Coalgebra in Computer SciencesNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:Familiarity with the algebraic and coalgebraic methods in computer science.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Backgrounds from the category theory: definition of the category, morphism, the concept

of production, coproduction, limit and colimit, functors, functors category, natural transformation.

- Bisimulation and Coinduction: bisimulation in modal logic and computer, fixed-point theorem, Relation Lifting, bisimulation and coinduction proof, algebraic properties of bisimulation.

- Introduction of coalgebra: algebraic and coalgebraic phenomena, inductive and coinductive definitions, algebra and induction, coalgebra and coinduction, coalgebraic process.

- Logic, Lifting, and Finality: distributive functors, Weak pullback, predicate and relation, relation lifting, logical bisimulation, polynomials and analytic functors.

- Advanced topics: Limits of coalgebra, invariants, predicate lifting, modal logic for coalgebra, temporal logic for coalgebra.

Grading Policy:




1- B. Jacobs, Introduction to Coalgebra: Towards Mathematics of States and Observation, Cambridge University Press, 2017.

2- D. Sangiorgi, Introduction to Bisimulation and Coinduction, Cambridge University Press, 2012.

3- D. Sangiorgi and J. Rutten, Advanced topics in bisimulation and coinduction, Cambridge University Press, 2012.

Name: Computability and ArithmeticNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: Advanced Theory of Computation

Course Objective:Learning some axiomatic approach towards the study of the computational classes.

Course Topics: 64 Theoretical hours, and 0 Practical hours- Preliminaries for the first-order intuitionistic logic,- Kripke models for the first-order intuitionistic logic,- Peano Arithmetic PA, Intuitionistic Arithmetic HA and Markov Arithmetic MA and their

relationship to the computability,- Kleene’s recursive realizability for the intuitionistic logic.- The Samuel Buss’s bounded arithmetic and its connection to the complexity classes P

and NP.

Grading Policy:




1- A.S. Troelstra and D. van Dalen, Constructivism in Mathematics, Vol 1, Elsevier, 1988.2- S. R. Buss, Bounded Arithmetic, Bibliopolis, Naples, Italy, 1986.

Name: Special Topics in Formal MethodsNumber of units: 4Unit type: 4 Theoretical units, 0 Practical units Type of course: OptionalPrerequisite courses: none

Course Objective:

In this course advanced topics in Formal Methods are introduced.



Grading Policy:





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