C O R E - P L U S M A T H E M A T I C S P R O J E C T

Scope & Sequencea l g e b r a a n d f u n c t i o n s

s t a t i s t i c s a n d p r o b a b i l i t y

g e o m e t r y a n d t r i g o n o m e t r y

d i s c r e t e m a t h e m a t i c s

ContemporaryMathematicsin ContextA Unified Approach

C O R E - P L U S M A T H E M A T I C S P R O J E C T

Scope and Sequence

ContemporaryMathematicsin ContextA Unified ApproachArthur F. CoxfordJames T. FeyChristian R. HirschHarold L. SchoenGail BurrillEric W. HartBrian A. KellerAnn E. WatkinswithMary Jo MessengerBeth E. RitsemaRebecca K. Walker

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written permission of the publisher.

Send all inquiries to:Glencoe McGraw-Hill8787 Orion PlaceColumbus, Ohio 43240-4027

ISBN 1-57039-895-X Contemporary Mathematics in ContextScope & Sequence

2 3 4 5 6 7 8 9 079 03 02 01

Glencoe/McGraw-Hill

This project was supported, in part, by the National Science Foundation.The opinions expressed are those of the authors and not necessarily those of the Foundation.

C P M P S c o p e a n d S e q u e n c e 5

Project DirectorChristian R. HirschWestern Michigan University

Project Co-DirectorsArthur F. CoxfordUniversity of Michigan

James T. FeyUniversity of Maryland

Harold L. SchoenUniversity of Iowa

Senior Curriculum DevelopersGail BurrillUniversity of Wisconsin-Madison

Eric W. HartWestern Michigan University

Brian A. KellerMichigan State University

Ann E. WatkinsCalifornia State University, Northridge

Professional Development CoordinatorBeth RitsemaWestern Michigan University

Evaluation CoordinatorSteven W. ZiebarthWestern Michigan University

Advisory BoardDiane BriarsPittsburgh Public Schools

Jeremy KilpatrickUniversity of Georgia

Kenneth RuthvenUniversity of Cambridge

David A. SmithDuke University

Edna VasquezDetroit Renaissance High School

Curriculum Development ConsultantsAlverna ChampionGrand Valley State University

Cherie CornickWayne County Alliance for Mathematics andScience

Edgar Edwards (Formerly) Virginia State Department ofEducation

Kenneth RossUniversity of Oregon

Richard ScheafferUniversity of Florida

Martha SiegelTowson University

Edward SilverUniversity of Pittsburgh

Lee StiffNorth Carolina State University

Paul ZornSt. Olaf College

Collaborating TeachersEmma AmesOakland Mills High School, Maryland

Cheryl Bach HeddenSitka High School, Alaska

Mary Jo MessengerHoward County Public Schools, Maryland

Valerie MillsAnn Arbor Public Schools, Michigan

Jacqueline StewartOkemos High School, Michigan

Michael VerkaikHolland Christian High School, Michigan

Marcia WeinholdKalamazoo Area Mathematics and ScienceCenter, Michigan

Graduate AssistantsCos FiUniversity of Iowa

Sarah FieldUniversity of Iowa

Kelly FinnUniversity of Iowa

Judy FlowersUniversity of Michigan

Johnette MassonUniversity of Iowa

Chris RasmussenUniversity of Maryland

Heather ThompsonIowa State University

Bettie TruittUniversity of Iowa

Roberto VillarubiUniversity of Maryland

Rebecca WalkerWestern Michigan University

Ed WallUniversity of Michigan

Technical CoordinatorJames LaserWestern Michigan University

Production and Support StaffKelly MacLeanJennifer RosenboomWendy WeaverKathryn WrightTeri ZiebarthWestern Michigan University

Catherine KernUniversity of Iowa

Software DevelopersJim FlandersColorado Springs, Colorado

Eric KamischkeInterlochen, Michigan

About the Core-Plus Mathematics ProjectThe Core-Plus Mathematics Project (CPMP) was funded by the National Science Foundationto develop student and teacher materials for a comprehensive Standards-based high school mathematics curriculum. Courses 1–3 comprise a core curriculum appropriate for all students.Course 4 continues the preparation of students for college mathematics.

C P M P S c o p e a n d S e q u e n c e 7

UNIFIED MATHEMATICSContemporary Mathematics in Context is a four-year unified curriculum thatreplaces the traditional Algebra-Geometry-Advanced Algebra/Trigonometry-Precalculus sequence. Each course features interwoven strands of algebra andfunctions, statistics and probability, geometry and trigonometry, and discretemathematics. Each of these strands is developed within focused units connectedby fundamental ideas such as symmetry, functions, matrices, and data analysisand curve-fitting. The largest number of units is devoted to algebra and functions.By encountering mathematics every year from a more mathematically sophisticatedpoint of view, students’ understanding of the strands deepen across the four-yearcurriculum. Mathematical connections between strands and ways of thinkingmathematically that are common across strands are emphasized. These mathe-matical habits of mind include visual thinking, recursive thinking, searching for and explaining patterns, making and checking conjectures, reasoning withmultiple representations, and providing convincing arguments and proofs.

The algebra and functions strand develops student ability to recognize, represent,and solve problems involving relations among quantitative variables. Central tothe development is the use of functions as mathematical models. The key algebraicmodels in the curriculum are linear, exponential, power, polynomial, logarithmic,rational, and periodic functions. Each algebraic model is investigated in fourlinked representations—verbal, graphic, numeric, and symbolic—with the aid oftechnology. Attention is also given to modeling with systems, both linear andnonlinear, and to symbolic reasoning and manipulation.

The primary role of the statistics and probability strand is to develop student abilityto analyze data intelligently, to recognize and measure variation, and to understandthe patterns that underlie probabilistic situations. The ultimate goal is for students tounderstand how inferences can be made about a population by looking at a samplefrom that population. Graphical methods of data analysis, simulations, sampling,and experience with the collection and interpretation of real data are featured.

The primary goal of the geometry and trigonometry strand is to develop visualthinking and student ability to construct, reason with, interpret, and apply math-ematical models of patterns in visual and physical contexts. Activities includedescribing patterns with regard to shape, size, and location; representing patternswith drawings, coordinates, or vectors; predicting changes and invariants in shapes;and organizing geometric facts and relationships through deductive reasoning.

The discrete mathematics strand develops student ability to model and solveproblems involving enumeration, sequential change, decision making in finitesettings, and relationships among a finite number of elements. Topics includematrices, vertex-edge graphs, recursion, models of social decision making, andsystematic counting methods. Key themes are discrete mathematical modeling,existence (Is there a solution?), optimization (What is the best solution?), andalgorithmic problem solving (Can you efficiently construct a solution?).

Algebra and Functions

Geometry andTrigonometry

Statistics and Probability

Discrete Mathematics

8 C P M P S c o p e a n d S e q u e n c e

ORGANIZATION OF THE CURRICULUMThe first three courses in the Contemporary Mathematics in Context series provided a common core of broadly useful mathematics for all students. Theywere developed to prepare students for success in college, in careers, and indaily life in contemporary society. Course 4 formalizes and extends the coreprogram, with a focus on the mathematics needed to be successful in collegemathematics and statistics courses. Unit titles for the four-year curriculum aregiven in the following table.

Course 1 Course 21 Patterns in Data 1 Matrix Models

2 Patterns of Change 2 Patterns of Location, Shape, and Size

3 Linear Models 3 Patterns of Association

4 Graph Models 4 Power Models

5 Patterns in Space and 5 Network OptimizationVisualization

6 Exponential Models 6 Geometric Form and Its Function

7 Simulation Models 7 Patterns in Chance

CAPSTONE Planning a Benefits CAPSTONE Forests, the Environment,Carnival and Mathematics

Course 3 Course 41 Multiple-Variable Models 1 Rates of Change

2 Modeling Public Opinion 2 Modeling Motion

3 Symbol Sense and 3 Logarithmic Functions and Algebraic Reasoning Data Models

4 Shapes and Geometric 4 Counting ModelsReasoning

5 Patterns in Variation 5 Binomial Distributions and Statistical Inference

6 Families of Functions 6 Polynomial and Rational Functions

7 Discrete Models of Change 7 Functions and Symbolic Reasoning

CAPSTONE Making the Best of It: 8 Space GeometryOptimal Forms and 9 InformaticsStrategies

10 Problem Solving, Algorithms, and Spreadsheets

C P M P S c o p e a n d S e q u e n c e 9

The following charts provide an overview of the mathematical content and flowof Courses 1– 4 in the Contemporary Mathematics in Context curriculum. Thecharts are organized by mathematical strand: algebra and functions, statistics andprobability, geometry and trigonometry, and discrete mathematics. Each of thefour strands has been divided into major categories, and under each of these categories you will find the mathematical topics developed in the curriculum.

Many cells in the grid have either a “● ” or a “+” to indicate the units in which each topic is covered. The “● ” indicates focus; this means that the topicis initially developed or is extended beyond its initial development or use. The“+” indicates connection, which means that a conceptual basis for the topic isdeveloped, the topic is briefly introduced, or the topic is revisited and usedwithout further development.

The Strand Charts

10 C P M P S c o p e a n d S e q u e n c e

ALG

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C P M P S c o p e a n d S e q u e n c e 11

ALG

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12 C P M P S c o p e a n d S e q u e n c e

ALG

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C P M P S c o p e a n d S e q u e n c e 13

ALG

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14 C P M P S c o p e a n d S e q u e n c e

ALG

EB

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AN

D F

UN

CT

ION

S

Alg

eb

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Syste

ms

Rea

l nu

mb

ers

and

th

eir

pro

per

ties

Mat

rice

s an

d t

hei

r p

rop

erti

es

Tran

sfo

rmat

ion

s an

d t

hei

r p

rop

erti

es

Vect

ors

an

d t

hei

r p

rop

erti

es

Co

mp

lex

nu

mb

ers

and

th

eir

pro

per

ties

Set

s an

d s

et o

per

atio

ns

Inte

ger

s m

od

n a

nd

th

eir

pro

per

ties

Calc

ulu

s U

nd

erp

inn

ing

s

Rat

es o

f ch

ang

e

Max

ima

and

min

ima

Lim

its

Seq

uen

ces

and

ser

ies

Loca

l lin

eari

ty

Der

ivat

ive

fun

ctio

ns

Acc

um

ula

tio

n o

f ch

ang

e

Are

a u

nd

er a

cu

rve

Def

init

e in

teg

ral

12

34

56

7

+

+●

●

++

+

Co

urs

e 1

Co

urs

e 2

Co

urs

e 3

Co

urs

e 4

12

34

56

7

+ ●

● ++

++

+ ●+

+ + +

12

34

56

7

● ++

++

+●

++

++

● ●

●

12

34

56

78

910

++ +

●

+●

●

●●

+● ●

●+

++

++

●+

++

++

++

●

●●

+● ● ●

+●

●Fo

cus

+C

on

nec

tio

ns

C P M P S c o p e a n d S e q u e n c e 15

STA

TIS

TIC

S A

ND

PR

OB

AB

ILIT

Y

Un

ivari

ate

Data

Nu

mb

er li

ne

(do

t) p

lots

Mea

sure

s o

f ce

nte

r an

d t

hei

r p

rop

erti

es: m

ean

, med

ian

Bas

ic s

hap

es

Ske

wn

ess

and

sym

met

ry

His

tog

ram

s

Clu

ster

s, g

aps,

an

d o

utl

iers

Box

plo

ts

Lin

ear

tran

sfo

rmat

ion

s o

f d

ata

Ste

m-a

nd

-lea

f p

lots

Ran

ge

and

inte

rqu

arti

le r

ang

e (I

QR

)

Mea

n a

bso

lute

dev

iati

on

(M

AD

)

Perc

enti

les

and

qu

arti

les

Sta

nd

ard

dev

iati

on

an

d it

s p

rop

erti

es

Freq

uen

cy t

able

s

Sta

nd

ard

ized

or

z-sc

ore

s

Co

nce

pt

of

dis

trib

uti

on

Biv

ari

ate

Data

Sca

tter

plo

ts a

nd

ass

oci

atio

n

Plo

ts a

nd

tre

nd

s ov

er t

ime

Su

m o

f sq

uar

ed d

iffer

ence

s

Cen

tro

id

Leas

t sq

uar

es r

egre

ssio

n li

nes

Err

ors

of

pre

dic

tio

n a

nd

res

idu

als

No

nlin

ear

reg

ress

ion

Infl

uen

tial

po

ints

Sp

earm

an’s

ran

k co

rrel

atio

n c

oef

fici

ent

Sca

tter

plo

t an

d c

orr

elat

ion

mat

rice

s

Pear

son’

s co

rrel

atio

n c

oef

fici

ent

r

Exp

lan

ato

ry a

nd

res

po

nse

var

iab

les

Lurk

ing

var

iab

les

Cau

se-a

nd

-eff

ect

rela

tio

nsh

ips

Log

an

d lo

g-l

og

tra

nsf

orm

atio

ns

12

34

56

7

● ●+

+●

+●

+●

+● ● ● ● ● ● ● +

●

●●

●+

++

● + +●

++

●

Co

urs

e 1

Co

urs

e 2

Co

urs

e 3

Co

urs

e 4

12

34

56

7 + + +●

+ ● ●

●+

+ ● ● ●+

●+ ●

● ● ● ● ● ● ●

12

34

56

7

++ + ●

++

++

+ + + + ● ●

●● +

++

+● +

+ +●

12

34

56

78

910

+ + + + + + + + + ● ●

● + ● ● ● ● +

+

●

●Fo

cus

+C

on

nec

tio

ns

16 C P M P S c o p e a n d S e q u e n c e

STA

TIS

TIC

S A

ND

PR

OB

AB

ILIT

Y

Pro

bab

ilit

y

No

rmal

dis

trib

uti

on

Sim

ula

tio

n

Ran

dom

dig

it ta

bles

and

ran

dom

num

ber

gene

rato

rs

Law

of

Larg

e N

um

ber

s

Empi

rica

l (ex

peri

men

tal)

and

theo

retic

al p

roba

bilit

ies

Ind

epen

den

t ev

ents

Bin

om

ial d

istr

ibu

tio

n

Geo

met

ric

(wai

tin

g-t

ime)

dis

trib

uti

on

Mu

ltip

licat

ion

Ru

le f

or

ind

epen

den

t ev

ents

Geo

met

ric

(are

a) m

od

els

Co

nd

itio

nal

pro

bab

ility

Exp

ecte

d v

alu

e

Rar

e ev

ents

Sam

plin

g d

istr

ibu

tio

ns

Mu

tual

ly e

xclu

sive

eve

nts

Ad

dit

ion

Ru

le f

or

mu

tual

ly e

xclu

sive

eve

nts

Cen

tral

Lim

it T

heo

rem

Pro

bab

ility

dis

trib

uti

on

Gen

eral

mu

ltip

licat

ion

ru

le

Bin

om

ial p

rob

abili

ty f

orm

ula

No

rmal

ap

pro

xim

atio

n t

o a

bin

om

ial

Infe

ren

tial

Sta

tisti

cs

Pop

ula

tio

n v

s. s

amp

le

Co

nfi

den

ce in

terv

als

Mar

gin

of

erro

r

Co

ntr

ol (

run

) ch

arts

Test

s of

sig

nific

ance

incl

udin

g Ty

pe I

and

Type

II e

rror

s

Sta

tistic

al s

igni

fican

ce

One

sam

ple

z-te

st f

or a

pro

port

ion

Gen

eral

izab

ility

of

resu

lts

Su

rveys

Ch

arac

teri

stic

s o

f a

wel

l-d

esig

ned

su

rvey

Sam

ple

su

rvey

vs.

cen

sus

Sam

ple

siz

e

Sim

ple

ran

do

m s

amp

le

Bia

s in

su

rvey

met

ho

d

Res

po

nse

rat

e

12

34

56

7

++

● ● ● ● ● + + ●

Co

urs

e 1

Co

urs

e 2

Co

urs

e 3

Co

urs

e 4

12

34

56

7 + ● ● + ● ● ● ● ● + ●

+

12

34

56

7

●

+

+ ++

+ +●

+ ● ● + ●

●+

● ●

● +

●+

● ● ● ● ● ●

12

34

56

78

910

● ● + + ++

++

+●

++

++

++

● ● ● + + ● ●

●

● ● ● + + ● ● ● ● + + + ● ●

●Fo

cus

+C

on

nec

tio

ns

C P M P S c o p e a n d S e q u e n c e 17

STA

TIS

TIC

S A

ND

PR

OB

AB

ILIT

Y

Exp

eri

men

ts

Ch

arac

teri

stic

s o

f a

wel

l-d

esig

ned

exp

erim

ent

Trea

tmen

ts, c

on

tro

l gro

up

s, r

and

om

as

sig

nm

ent,

an

d r

eplic

atio

n

So

urc

e o

f b

ias

and

co

nfo

un

din

g, i

ncl

ud

ing

p

lace

bo

eff

ect

and

blin

din

g

Ran

do

miz

atio

n t

est

Larg

e sa

mp

le t

est

for

a d

iffer

ence

bet

wee

n

two

pro

po

rtio

ns

12

34

56

7C

ou

rse 1

Co

urs

e 2

Co

urs

e 3

Co

urs

e 4

12

34

56

71

23

45

67

12

34

56

78

910

● ● ● ● ●

●Fo

cus

+C

on

nec

tio

ns

18 C P M P S c o p e a n d S e q u e n c e

GE

OM

ET

RY

AN

D T

RIG

ON

OM

ET

RY

Th

ree-d

imen

sio

nal

Sh

ap

es

Reg

ula

r (P

lato

nic

) so

lids

Rig

ht

po

lyg

on

al p

rism

s an

d p

yram

ids

Co

nes

an

d c

ylin

der

s

Ske

tch

ing

sh

apes

Rig

idit

y

Bila

tera

l sym

met

ry

Cro

ss s

ecti

on

s

Co

nto

ur

dia

gra

ms

Su

rfac

es

Su

rfac

es o

f re

volu

tio

n

Cyl

ind

rica

l su

rfac

es

Tw

o-d

imen

sio

nal

Sh

ap

es

Def

init

ion

s o

f p

oly

go

ns

Cha

ract

eris

tics

of p

olyg

ons

and

spec

ial q

uadr

ilate

rals

Bila

tera

l an

d r

ota

tio

nal

sym

met

ry

Tran

slat

ion

al s

ymm

etry

An

gle

su

ms

of

po

lyg

on

s

Tess

ella

tio

ns

Co

ng

ruen

ce

Pro

per

ties

of

par

alle

log

ram

s

Sim

ilari

ty

Mo

del

ing

pla

ne

shap

es w

ith

co

ord

inat

es

Tria

ng

ula

r an

d q

uad

rila

tera

l lin

kag

es

Measu

res

Are

a

Peri

met

er

Pyt

hag

ore

an T

heo

rem

Volu

me

Su

rfac

e ar

ea

Rad

ian

an

d d

egre

e m

easu

re

An

gu

lar

velo

city

Lin

ear

velo

city

12

34

56

7

+● ● ● ● ● ● ● ● ● ● ● ● + +

+●

++

● ● ● ● +

Co

urs

e 1

Co

urs

e 2

Co

urs

e 3

Co

urs

e 4

12

34

56

7

+

●+

++

++

++

++

●+

●

●

+ ●

++

+● +

● ● ●

12

34

56

7

●

++

+ ●

+●

+●

++

+ ++

+

+●

++ +

+

12

34

56

78

910

+ + ● ● ● ● ● ● ●

++ +

●+

++

++

++ +

++

++

●●

●

●Fo

cus

+C

on

nec

tio

ns

C P M P S c o p e a n d S e q u e n c e 19

GE

OM

ET

RY

AN

D T

RIG

ON

OM

ET

RY

Co

ord

inate

Mo

dels

an

d G

rap

hs

Co

ord

inat

e g

rap

hs

Geo

met

ry o

f fu

nct

ion

gra

ph

s

Slo

pe

of

a lin

e

Eq

uat

ion

s o

f lin

es

Slo

pes

of

par

alle

l an

d p

erp

end

icu

lar

lines

Dis

tan

ce a

nd

mid

po

int

form

ula

s

Co

ord

inat

e re

pre

sen

tati

on

of

tran

sfo

rmat

ion

s

Co

ng

ruen

ce a

nd

sim

ilari

ty

Mat

rix

rep

rese

nta

tio

n o

f p

oly

go

ns

Co

ord

inat

e p

roo

f

Vect

ors

3-d

imen

sio

nal

co

ord

inat

e g

rap

hs

Ske

tch

ing

su

rfac

es in

3-d

imen

sio

nal

sp

ace

Eq

uat

ion

s o

f su

rfac

es

Eq

uat

ion

s o

f p

lan

es

Trac

es o

f su

rfac

es

Tra

nsfo

rmati

on

s a

nd

Sym

metr

ies

Bila

tera

l an

d r

ota

tio

nal

sym

met

ry

Frac

tals

Tran

slat

ion

al s

ymm

etry

Tess

ella

tio

ns

Str

ip p

atte

rns

Iso

met

ric

tran

sfo

rmat

ion

s

Siz

e tr

ansf

orm

atio

ns

Mat

rix

rep

rese

nta

tio

n o

f tr

ansf

orm

atio

ns

Tran

sfo

rmat

ion

of

gra

ph

s an

d f

un

ctio

n r

ule

s

Co

mp

lex

nu

mb

er o

per

atio

ns

and

tra

nsf

orm

atio

ns

12

34

56

7

●●

++

●

+●

++

● ● ● ●

++

+

Co

urs

e 1

Co

urs

e 2

Co

urs

e 3

Co

urs

e 4

12

34

56

7

++

++

●● ● ● ● ● ● +

+

+ ● ●+

●

● ++

12

34

56

7

++

● ●

++

●

++

++

●+

++

+ ++

+

●●

12

34

56

78

910

++

+● ●

++

++

++

●+

+ ++

●

●+

+● ● ● ● ● +

++

+

+●

●+

+●

●Fo

cus

+C

on

nec

tio

ns

20 C P M P S c o p e a n d S e q u e n c e

GE

OM

ET

RY

AN

D T

RIG

ON

OM

ET

RY

Tri

go

no

metr

y

Peri

od

ic c

han

ge

Tria

ng

ula

r lin

kag

es w

ith

on

e va

riab

le s

ide

Trig

onom

etric

ratio

s an

d fu

nctio

ns (s

ine,

cos

ine,

and

tang

ent)

Ind

irec

t m

easu

rem

ent

(an

gle

s an

d le

ng

ths)

Cir

cula

r an

d p

erio

dic

mo

tio

n

Peri

od

Peri

od

ic m

od

els

Trig

on

om

etri

c g

rap

hs

Rad

ian

an

d d

egre

e m

easu

re

Am

plit

ud

e

Law

of

Co

sin

es

Law

of

Sin

es

Co

mp

on

ent

anal

ysis

of

vect

ors

Inve

rse

trig

on

om

etri

c fu

nct

ion

s

Trig

on

om

etri

c id

enti

ties

Trig

on

om

etri

c ra

tio

s an

d f

un

ctio

ns

(sec

ant,

co

seca

nt,

an

d c

ota

ng

ent)

Reaso

nin

g a

nd

Pro

of

Ind

uct

ive

reas

on

ing

Co

un

tere

xam

ple

s

Ded

uct

ive

reas

on

ing

Des

ign

ing

an

d p

rog

ram

min

g a

lgo

rith

ms

Co

ord

inat

e an

d a

nal

ytic

pro

of

Syn

thet

ic p

roo

f

Ass

um

pti

on

s in

pro

of

Prin

cip

les

of

log

ic

Co

nver

se

An

gle

rel

atio

ns

for

two

inte

rsec

tin

g li

nes

An

gle

rel

atio

ns

for

thre

e in

ters

ecti

ng

lin

es

Para

llelis

m

Sim

ilari

ty c

on

dit

ion

s fo

r tr

ian

gle

s

Co

ng

ruen

ce c

on

dit

ion

s fo

r tr

ian

gle

s

Nec

essa

ry a

nd s

uffic

ient

con

ditio

ns fo

r pa

ralle

logr

ams

Geo

met

ric

con

stru

ctio

ns

Vect

or

pro

of

12

34

56

7

+

+

++

++

++

++

+ +

Co

urs

e 1

Co

urs

e 2

Co

urs

e 3

Co

urs

e 4

12

34

56

7

● ● ● ● ● ● ● ● ● ● +

++

++

++

++

++

+●

++

●+

●

12

34

56

7

+●

+ ++

●+ +

●

+●

+●

+● + ●

●●

+●

++

++

+

++

+●

++

++

+●

++

●+

●● ● ● ● ● ● ● ● ● ● ● ●

12

34

56

78

910

●●

●

++ ●

●

●●

+●

●

●+

+●

+●

●

+●

+ + ●

+● ● ●

++

++

++

++

++

++

++

++

++

+●

+ +●

●

++

++

●

●Fo

cus

+C

on

nec

tio

ns

C P M P S c o p e a n d S e q u e n c e 21

DIS

CR

ET

E M

AT

HE

MA

TIC

S

Vert

ex-E

dg

e G

rap

hs

Vert

ex-e

dg

e g

rap

h m

od

els

Dig

rap

hs

Ad

jace

ncy

mat

rice

s fo

r ve

rtex

-ed

ge

gra

ph

s

Eu

ler

pat

hs

and

cir

cuit

s

Gra

ph

co

lori

ng

Cri

tica

l pat

h a

nal

ysis

an

d P

ER

T c

har

ts

Tree

s an

d m

inim

al s

pan

nin

g t

rees

Sh

ort

est

pat

hs

Ham

ilto

nia

n p

ath

s an

d c

ircu

its

Recu

rsio

n a

nd

Ite

rati

on

Rep

rese

nta

tio

n u

sin

g t

he

wo

rds

NO

W a

nd

NE

XT

Rep

rese

nta

tio

ns

of

linea

r fu

nct

ion

s

Rep

rese

nta

tio

ns

of

exp

on

enti

al f

un

ctio

ns

Rec

urs

ion

eq

uat

ion

s (d

iffer

ence

eq

uat

ion

s)

Frac

tals

Co

mp

osi

tio

n o

f fu

nct

ion

s

Seq

uen

ces

and

ser

ies

Fun

ctio

n it

erat

ion

Fin

ite

diff

eren

ces

Fixe

d p

oin

ts

Gra

ph

ical

iter

atio

n

Matr

ices

Ad

jace

ncy

mat

rice

s fo

r ve

rtex

-ed

ge

gra

ph

s

Mat

rix

mo

del

s

Ro

w a

nd

co

lum

n s

um

s

Mat

rix

add

itio

n

Sca

lar

mu

ltip

licat

ion

Mat

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Item No. 39895 ISBN 1-57039-895-X