cohtran-SEMESTER COURSES

SPRING SEMESTER 2011 2010 2009 

FALL SEMESTER 2008

COURSE SYLLABUS

MATHEMATICS

Lecturer : MSc Math-Mech TRAN HONG CO .

Introduction

The goal of this course is to expose students to topics in Mathematics that are often used in scientific approaches especially in economic and business management . The mathematic course contains many problems from the basic to the advanced, to supply student with  a wide range of abilities and interests. Beside some of the examples are simply designed to build skills, every effort has been made to generalize problems, so that students can see common uses and practical applications of the mathematics they are studying, and appreciate the power of mathematics. We hope that students will be able to seize the essence of all the matters and also make use of mathematical concepts to the realities .  

Objectives

There are three objectives  :

1                    To introduce the basic concepts in mathematics : sets , counting and logic . From the such essentials , the students would be provided knowledge to access data with combinatorics , probability and financial tools .

2                    Considering the operations        and applications of matrices  . The students would be communicated key concepts in linear algebra and usefulness of matrices for solving the optimization problem and prediction by Markov’s chains .

3                    To provide the concepts in calculus and applications to the students briefly but completely including limitation , differentiation and integration .

Materials

Students can refer to materials as following -Mathematics – A practical course , Co.H.Tran MMPC-VN , 2008 -Mathematics for the international student , Paul Urban , Haese-Harris

Publications , 2004 . -Calculus I , Paul Dawkins , 2007 . -Business Calculus Demystify , Rhonda HuettenMueller , Mc Graw-

Hill , 2006 . -Mathematics –A practical Odyssey , David B. Johnson , Thompson-Brooks/Cole , 2005 .

Contents

Mathematics is a 16-week course , including 7 chapters , 5 home assignments , a midterm and final test . 

Chapter 1 . LOGIC , SETS  AND COUNTING

1.1 SETS – BINARY OPERATIONS

1.2 SYMBOLIC LOGIC – BICONDITIONAL

                        1.3 COUNTING - COMBINATORIAL LOGIC

                        Chapter 2 . PROBABILITY , STATISTICS AND FINANCE .

2                     PROBABILITY - COMBINATORICS –EXPECTED  VALUE

2. 2 STATISTICS , LINEAR REGRESSION

                        2. 3 FINANCE

                        Chapter 3 . GEOMETRY

2                     GEOMETRICAL FORMULAS

3.2 POLYGON GEOMETRY

3.3 SPACE SOLID GEOMETRY

3.4 2D AND 3D COORDINATE SYSTEMS

3.5 TRIGONOMETRY

                        3.6 CONIC

                        Chapter 4 . LINEAR ALGEBRA

2                     MATRICES – BASIC OPERATIONS

4.2 INVERSE MATRICES – MATRIX EQUATIONS

4.3 SYSTEMS OF LINEAR EQUATIONS WITH NON-UNIQUE SOLUTIONS

4.4 SYSTEMS OF LINEAR INEQUALITIES

4.5 LINEAR PROGRAMMING , GRAPHICAL METHODS

                        4.6 MARKOV CHAINS

                        CHAPTER 5 . EXPONENTIAL AND LOGARITHM

2                     EXPONENTIAL FUNCTIONS

5.2 LOGARITHMIC FUNCTIONS

5.3 SOLVING EXPONENTIAL EQUATIONS – LOGARITHMIC EQUATIONS

                        5.4 EXPONENTIAL AND LOGARITHMIC MODELS

                        CHAPTER 6 . CALCULUS

2                     SEQUENCES - DISCRETE FUNCTIONS

6.2 SERIES

6.3 LIMITS OF FUNTIONS

6.4 THE DERIVATIVE

                        6.5 THE INTEGRATION

                        CHAPTER 7 . APPLICATIONS OF DERIVATIVES AND INTEGRATIONS

2                     APPLICATIONS OF DERIVATIVES

7.2 APPLICATIONS OF DERIVATIVES ( cont )

7.3 APPLICATIONS OF INTEGRATIONS

7.4 APPLICATIONS OF INTEGRATIONS (cont)

Assignments

There are 5 home assignments based on the topics in chapters above . 

HOME ASSIGNMENT 1

1                    LOGIC , SET , COUNTING 

2                     PROBABILITY , STATISTICS 

HOME ASSIGNMENT 2

1. FINANCE
2 .GEOMETRY

HOME ASSIGNMENT 3

1                    GEOMETRY

2                    LINEAR ALGEBRA

HOME ASSIGNMENT 4

1                    EXPONENTIAL AND LOGARITHM

2                    CALCULUS

HOME ASSIGNMENT 5

1                    LIMITS

2                    DERIVATIVE

3                    INTEGRATION

Examinations

The midterm and final test are open-book examinations and 1 ½  hours long both . The midterm covers chapters 1 – 4 , and final covers chapters 5 – 7 .

Grading

The final grade will be determined as follows 

TOTAL HOME ASSIGNS SCORES  30% 
MIDTERM SCORES 35%
FINAL SCORES  35%

Calendar

____________________________________________________________________________________________________________________________   

View the  Mathematics Course Syllabus online                                                                               Mathematics  - COHONGTRAN  ( Read online ) 

COURSE SYLLABUS

COLLEGE ALGEBRA

Lecturer :  TRAN HONG CO .

Introduction

The purpose of this course is to provide an understanding of the basic concepts of equation , inequality   , especially to the polynomial, exponential, and logarithmic functions  The students will have ability to solve system of equations , linear programming problems by using matrices . Some of methods used in linear regression , interpolation and extrapolation will be also presented particularly  .  

The subjects considered in this course would be described not only as mathematical methods , explaining the principles , dealing with the formulas but also as applications handled by softwares . There are many examples that are given to illustrate the use of formulas and apply the mathematical models to the reality .The discussion is based on a course of 39 lectures followed by the curricular below  .

Objectives

There are three objectives  :

1.  To introduce the basic concepts in algebra  : functions , mathematical models – how to describe and sketch the graphs  . From the such essentials , the students would be provided knowledge to access data , determine the models fitted  with common mathematical tools .

2.  To provide ability in solving linear and non –linear equations and  inequalities in one variable, Students will be able to simplify and evaluate expressions , set up mathematical models that are compatible with the raw data .

3.  To guild students to the meaning of matrix , matrix operations  and using matrices for the models , how to solve the system of linear equations in 2 or 3 variables  , the linear optimization problems .

After completing this course, students will be able to :

1. Identify the domain and range of various functions and sketch their graphs.

2. Determine equations for lines , curves and sketch graphs of the best fitted curves .

3. Set up and solve  the linear and non-linear equations/inequalities .

4. Determine and solve systems of linear equations in two or three variables by using matrices

5. Solve application problems in linear optimization  .

Evaluation of Ability

1. Writing skill : Students must use proper spelling and grammar on home assignments , presentations and tests . Proper use of mathematical symbols will be also required for doing works .

2. Reading skill : All presentations and homework assignments include reading the appropriate section and chapter of the textbook as well as completing the problems assigned  .

3. Integrate learning skill: Students will solve problems involving applications of other areas , also need to know the organization of group activities to solve the exercises.

4. Creativity: The student will sketch out a plan of using mathematical knowledge before developing a suitable solution for a problem .
5. Ethics : The students must self-perform the exercises punctually . Plagiarism and cheating of any kind will be rejected.

Materials

Students can refer to materials as following

- Essentials of College Algebra with Modelling and Visualization  , G. Rockswold , Addison Wesley Publishing Co., Boston MA , 3^th Ed , 2008 .

- Algebra & Trigonometry: Graphs and Models, Bittinger, Beecher, Ellenbogen and Penna, Addison-Wesley Publishing Co., 2^nd  Ed  , 2001 .

- College Algebra  lectures  ,  CoHongTran , 2008

Softwares

- Maple  versions  6 , 9.5 , 10 or higher   .

- Excel  2003 .

- MathProf  version 4.0

Contents

College Algebra is a 16-week course , 4 hours per week  , including 6  chapters , 10  home assignments , 6 presentations ,  a midterm and final test  . 

CHAPTER 1

1.1 FUNTIONS –GRAPHS .

1.2 GRAPHS OF FUNTIONS –MATHEMATICAL MODELS .

1.3 LINEAR FUNCTIONS .

1.4 EQUATIONS OF LINES –RATE OF CHANGE .

1.5 ALGEBRAIC AND GRAPHICAL SOLUTIONS OF LINEAR EQUATIONS .

1.6 FITTING LINES TO THE DATA POINTS –MODELING LINEAR FUNCTIONS.

1.7 MODELS IN BUSINESS AND ECONOMICS .

1.8 SOLUTIONS OF LINEAR INEQUALITIES . 

CHAPTER 2

2.1 QUADRATIC FUNCTIONS –PARABOLAS .

2.2 SOLVING QUADRATIC EQUATIONS .

2.3 POWER FUNCTIONS AND TRANSFORMATION .

2.4 QUADRATIC AND POWER MODELS .

2.5 COMBINING FUNCTIONS –RECIPROCAL , ABSOLUTE , PIECEWISE DEFINED FUNCTIONS .

2.6 INVERSE FUNCTIONS .

2.7 QUADRATIC AND POWER INEQUALITIES .

CHAPTER 3

3.1 EXPONENTIAL FUNCTIONS .

3.2 LOGARITHMIC FUNCTIONS.

3.3 SOLVING  EXPONENTIAL EQUATIONS – PROPERTIES OF LOGARITHMS .

3.4 EXPONENTIAL AND LOGARITHMIC MODELS .

3.5 EXPONENTIAL FUNCTIONS –INVESTING .

3.6 ANNUITIES –LOAN REPAYMENTS .

3.7 LOGISTIC AND GOMPERTZ FUNCTIONS .

CHAPTER 4

4.1 HIGHER DEGREE POLYNOMIAL FUNCTIONS .

4.2 MODELING CUBIC AND QUARTIC FUNCTIONS .

4.3 SOLUTIONS OF POLYNOMIAL EQUATIONS .

4.4 SOLUTIONS OF POLYNOMIAL EQUATIONS BY USING SYNTHETIC DIVISION .

4.5 COMPLEX SOLUTIONS –FUNDAMENTAL THEOREM OF ALGEBRA .

4.6 RATIONAL FUNCTIONS AND RATIONAL EQUATIONS .

4.7 POLYNOMIAL AND RATIONAL INEQUALITIES .

CHAPTER 5

5.1 SYSTEMS OF LINEAR EQUATIONS IN 2 VARIABLES .

5.2 SYSTEMS OF LINEAR EQUATIONS IN 3 VARIABLES , MATRIX SOLUTION.

5.3 SYSTEMS OF LINEAR EQUATIONS WITH NON-UNIQUE SOLUTIONS .

5.4 MATRICES –BASIC OPERATIONS .

5.5 INVERSES MATRICES –MATRIX EQUATIONS .

CHAPTER 6

6.1 SYSTEMS OF LINEAR INEQUALITIES .

6.2 LINEAR PROGRAMMING –GRAPHICAL METHODS .

6.3 SEQUENCES –DISCRETE FUNCTIONS .

6.4 SERIES .

6.5 PREPARING FOR CALCULUS .

Assignments

There are 10 home assignments based on the topics in chapters above . 

            HOME ASSIGNMENT 1

1                    FUNCTION – GRAPHS –MATHEMATICAL MODELS .

2                    SOLUTIONS  OF LINEAR EQUATIONS AND INEQUALITIES  . 

            HOME ASSIGNMENT 2

1                     LINEAR REGRESSION –BEST FITTED LINE .

2                    LINEAR MODELS IN BUSINESS AND ECONOMICS . 

            HOME ASSIGNMENT 3

1        QUADRATIC AND POWER FUNCTIONS .
2        COMBINING AND INVERSE  FUNCTIONS  .
3        SOLVING QUADRATIC EQUATIONS AND INEQUALITIES .

           HOME ASSIGNMENT 4

1                    EXPONENTIAL , LOGARITHMIC , LOGISTIC AND   

          GOMPERTZ FUNCTIONS .

2                    SOLUTIONS  OF EXPONENTIAL , LOGARITHMIC EQUATIONS / 

         INEQUALITIES .   

3       APPLICATIONS OF  EXPONENTIAL , LOGARITHMIC , LOGISTIC AND 

          GOMPERTZ  MODELS .

            HOME ASSIGNMENT 5

1                    HIGHER DEGREE POLYNOMIAL AND RATIONAL FUNCTIONS .

2                    SOLVING THE HIGHER DEGREE POLYNOMIAL AND RATIONAL

          EQUATIONS / INEQUALITIES .

           HOME ASSIGNMENT  6

1              MATRICES – BASIC OPERATIONS .

2          GAUSS –JORDAN  ELIMINATION .

           HOME ASSIGNMENT 7

1         SYSTEM OF LINEAR EQUATIONS .

2         MATRIX EQUATIONS –INVERSE MATRIX .

           HOME ASSIGNMENT 8

1        MATRIX EQUATIONS WITH TECHNOLOGY .

2        SOLVING  MATRIX EQUATIONS .

           HOME ASSIGNMENT 9

1         SYSTEM OF LINEAR INEQUALITIES .

2         LINEAR PROGRAMMING .  

           HOME ASSIGNMENT 10

1         ARITHMETIC AND GEOMETRIC SEQUENCES .

2         DISCRETE FUNCTIONS - APPLICATIONS .

Examinations

The midterm and final test are 2 -hour examinations . The midterm covers chapters 1 – 3 , and the final covers chapters 4 – 6 .

Grading

The final grade will be determined as follows 

ATTENDANCE   10%

PRESENTATION  10%

TOTAL HOME ASSIGNS SCORES  20% 
MIDTERM SCORES 20%
FINAL SCORES  40%

Calendar

 ____________________________________________________________________________________________________________________________ 

 View the  College Algebra Course Syllabus online   

-----------------------------------------------------------------------------

SUMMER SEMESTER 2008

SUMMER SEMESTER 2009 2010

COURSE SYLLABUS

BUSINESS  MATHEMATICS

Lecturer :  TRAN HONG CO .

Introduction

The purpose of this course is to help students understand concepts covered in business mathematics to solve problems and  also  to provide applications on the  arithmetics , statistics and pre-calculus , adapted to the demand of students with the average level on mathematical knowledge and tools.

The subjects considered in the business mathematics course would be described not only as mathematical methods but also as applications handled by softwares . The lecturer 's intention is to explain the calculating principles , to deal with the formulas , validity of the methods and mathematical tools in business . There are many examples that are given to illustrate the use of formulas and apply the mathematical models to the reality .The discussion is based on a course of 43 lectures on fundamentals of mathematics which the students have learnt in the first years .To make the knowledge easy to know, some ideas will be covered in each section and connected reasonably , strictly throughout the course  .

Objectives

There are three objectives  :

1.  To introduce the basic concepts in arithmetics : whole number , decimal and fraction , finding part , base and rate – how to know and solve the decrease and increase problems . From the such essentials , the students would be provided knowledge to access data with common arithmetic tools .

2.  Considering the banking activities through concepts and documentation , checking account , check registers , checking services , simple and compound interest , loan and credit . Moreover  students would be habituated the key concepts in wage control , taxes and insurance , stock and bond  .

 3.  Providing  the concepts in business activities , mark-up and mark-down , invoice and trade discount . Students would approach the essentials  and applications on depreciation , the income statement , balance sheet and analyzing methods . Some topics in statistics are also discussed such as probability , distribution ,mean , mode and median  .

Materials

Students can refer to materials as following

- Business Mathematics , Miller Salzman Clendenen , 9^th Ed , 2004 .

- Mathematics for Business , Science and Technology , Steven T. Karris , Orchard Publication , 2^nd  Ed , 2003 .

- Business Calculus Demystify , Rhonda HuettenMueller , Mc Graw- Hill , 2006 .

- Business Mathematics lectures  ,  Co.H.Tran MMPC-VN , 2008

Softwares

- Maple  versions  6 , 9.5 , 10 or higher   .

- Excel  2003 .

- ESBStats version 2.2

- ESBPDF Analysis version 1.4

- APRWIN  version 6.2

- Financial Calculators , On line Tools , KJE  .

 Contents

Business Mathematics is a 10-week course, 6 hours per week  , including 15  chapters , 7  home assignments , 5 presentations ,  a midterm and final  test  . 

CHAPTER 1

1.1 WHOLE NUMBERS - APPLICATION .

1.2 DECIMALS - ADDITION AND SUBTRACTION .

CHAPTER 2

2.1 FRACTIONS - ADDITION AND SUBTRACTION .

2.2 MIXED NUMBERS -MULTIPLICATION AND DIVISIONCONVERTING.

CHAPTER 3

3.1 WRITING DECIMALS AND FRACTIONS AS PERCENTS

3.2 FINDING PARTS - BASES .

3.3 INCREASE AND DECREASE PROBLEMS .

CHAPTER 4

4.1 CHECKING ACCOUNTS AND CHECK REGISTERS .

4.2 CHECKING SERVICES AND CREDIT-CARD TRANSACTION .

4.3 RECONCILIATION .

CHAPTER 5

5.1 GROSS EARNINGS : WAGES AND SALARIES .

5.2 GROSS EARNINGS : PIECEWORK AND COMMISSIONS .

5.3 SOCIAL SECURITY , MEDICARE , OTHER TAXES .

5.4 INCOME TAX WITHHOLDING .

CHAPTER 6

6.1 INVOICES AND TRADE DISCOUNTS .

6.2 SINGLE DISCOUNT EQUIVALENTS .

6.3 CASH DISCOUNTS .

6.4 CASH DISCOUNTS FROM OTHER METHODS .

CHAPTER 7

7.1 MARKUP ON COSTS .

7.2 MARKUP ON SELLING PRICE .

7.3 MARKDOWN .

7.4 TURNOVER AND VALUATION OF INVENTORY .

CHAPTER 8

8.1 BASIC CONCEPTS OF SIMPLE INTEREST .

8.2 FINDING PRINCIPAL , RATE , AND TIME .

8.3 SIMPLE DISCOUNT NOTES .

8.4 DISCOUNTING A NOTE BEFORE MATURITY .

CHAPTER 9

9.1 COMPOUND INTEREST .

9.2 INTEREST BEARING BANK ACCOUNTS – INFLATION .

9.3 PRESENT VALUE .

CHAPTER 10

10.1 ANNUITIES – RETIREMENT ACCOUNTS .

10.2 PRESENT VALUE OF ANNUITY ACCOUNTS – SINKING FUNDS – TAX DEFERRED ANNUITY .

 10.3 STOCKS AND BONDS .

CHAPTER 11

11.1 CREDITS – CHARGE CARDS – LOANS .

11.2 PERSONAL PROPERTY LOANS – REAL ESTATE

LOANS .

CHAPTER 12

12.1 PROPERTY TAX – PERNONAL INCOME TAX .

12.2 FIRE INSURANCE –MOTOR –VEHICLE INSURANCE .

12.3 LIFE INSURANCE .

CHAPTER 13

13.1 DEPRECIATION : STRAIGHT _ LINE METHOD &

DECLINING – BALANCE METHOD .

13.2 DEPRECIATION : SUM OF THE YEARS DIGITS

METHOD – UNITS OF PRODUCTION METHOD – MACRS .

CHAPTER 14

14.1 THE INCOME STATEMENT AND ANALYZING THE INCOME STATEMENT .

14.2 THE BALANCE SHEET AND ANALYZING THE BALANCE SHEET .

CHAPTER 15

15.1 FREQUENCY - DISTRIBUTION .

15.2 MEAN – MEDIAN – MODE .

Assignments

There are 7 home assignments based on the topics in chapters above . 

HOME ASSIGNMENT 1

1                    WHOLE NUMBER , DECIMAL AND  FRACTION .

2                    RATE  ,  PART  AND  BASE .

3                    PERCENTAGE PROBLEMS . 

HOME ASSIGNMENT 2

1        CHECKING ACCOUNT , CHECK REGISTERS AND SERVICES .
2        RECONCILIATION .
3        WAGE , SOCIAL SECURITY , MEDICARE AND TAXES .

HOME ASSIGNMENT 3

1                    INVOICE – TRADE DISCOUNT , CASH DISCOUNT .

2                    MARK UP , MARK DOWN .

3                    TURN OVER – VALUATION OF INAVENTORY .

HOME ASSIGNMENT 4

1                    SIMPLE – COMPOUND INTEREST 

2                    SIMPLE DISCOUNT – PRESENT VALUE .

HOME ASSIGNMENT 5

1                    ANNUITY – SINKING FUND  

2                    STOCK – BOND

3                    CREDIT – LOAN

HOME ASSIGNMENT  6

1         TAX – INSURANCE

2         DEPRECIATION

HOME ASSIGNMENT 7

1         INCOME STATEMENT – BALANCE SHEET

2         FREQUENCY – DISTRIBUTION

3.        MEAN ,  MODE , MEDIAN .

Examinations

The midterm and final test are open-book examinations and 1 ½  hours long both . The midterm covers chapters 1 – 7 , and final covers chapters 8 – 15 .

Grading

The final grade will be determined as follows 

ATTENDANCE   10%

PRESENTATION  10%

TOTAL HOME ASSIGNS SCORES  20% 
MIDTERM SCORES 20%
FINAL SCORES  40%

Calendar

 ____________________________________________________________________________________________________________________________