BS Math 3rd Semester

BS Mathematics (Semester Plan)

The BS Mathematics degree program is divided into eight semesters as follows.

Code

Course Title

CrHr

Pre-Req

 

Code

Course Title

CrHr

Pre-Req

Year 1 Semester 1

 

Year 1 Semester II

XXX***

UR-I

4(3+1)

None

 

MATH102

Calculus-II

3(3+0)

MATH101

MATH101

Calculus-I

3(3+0)

None

 

MATH103

Discrete Mathematics

3(3+0)

None

XXX***

UR-II

3(3+0)

None

 

XXX***

UR-IV

3(3+0)

None

XXX***

UR-III

3(3+0)

None

 

XXX***

UR-V

3(3+0)

None

XXX***

FR-I

3(3+1)

None

 

XXX***

FR-II

4(3+1)

None

Year 2 Semester III

 

Year 2 Semester IV

MATH201

Calculus-III

3(3+0)

MATH102

 

MATH211

Group Theory

3(3+0)

None

XXX***

FR-III

3(3+0)

MATH101

 

MATH271

Ordinary Differential Equations

3(3+0)

MATH101

MATH202

Number Theory

3(3+0)

None

 

MATH212

Linear Algebra

3(3+0)

None

XXX***

FR-IV

3(3+0)

None

 

XXX***

FR-V

3(3+0)

None

XXX***

UR-VI

3(3+0)

None

 

XXX***

FR-VI

3(3+0)

None

XXX***

UR-VII

3(3+0)

None

 

XXX***

FR-VII

3(2+1)

None

Year 3 Semester V

 

Year 3 Semester VI

MATH325

Vector and Tensor Analysis

3(3+0)

MATH212

 

MATH322

Real Analysis – II

3(3+0)

MATH321

MATH321

Real Analysis-I

3(3+0)

MATH101

 

MATH331

Numerical Analysis – I

4(3+1)

MATH321

MATH351

General Topology

3(3+0)

None

 

MATH332

Complex Analysis

3(3+0)

MATH321

MATH371

Partial Differential Equations

3(3+0)

MATH271

 

MATHxxx

Elective-II

3(3+0)/4(3+1)

MATHxxx

MATH313

Rings & Fields

3(3+0)

MATH211

 

MATHxxx

Elective-III

3(3+0)/4(3+1)

MATHxxx

MATHxxx

Elective-I

3(3+0)/4(3+1)

MATHxxx

 

 

 

 

 

Year 4 Semester VII

 

Year 4 Semester VIII

MATH471

Mathematical Modeling

3(3+0)

MATH271/MATH212

 

MATH472

Integral Equations

3(3+0)

MATH271

MATH424

Functional Analysis

3(3+0)

MATH212

 

MATH451

Differential Geometry

3(3+0)

MATH351

MATH431

Numerical Analysis-II

4(3+1)

MATH331

 

MATHxxx

Elective-IV

3(3+0)/4(3+1)

MATHxxx

MATHXXX/
MATH493

Elective/Report Writing & Presentation
Skills

3(3+0)/4(3+1)

MATHxxx

 

MATHxxx

Elective-V

3(3+0)/4(3+1)

MATHxxx


MATHXXX/
MATH499

Elective/Senior Design Project-I

3(0+9)/3(3+0)/4(3+1)

MATHxxx

 


MATHXXX/
MATH499

Elective/Senior Design Project-II

3(0+9)/3(3+0)/

4(3+1)

MATHxxx

                   

Note:   UR:          University Requirement Courses,    FR: Faculty Requirement Courses

Course Code:  MATH201

Course Title:  Calculus-III

Credit Hours:               (3 0 3)

Pre-requisite(s):         MATH102

 Course Objectives:

 The objectives of this course are:

  1. To apply previously developed skills learned in Calculus to learn Multivariable Calculus and Vectors
  2. To cover Vectors, Partial Derivatives, Multiple Integrals and Vector Fields in order to prepare students for further study in technological disciplines.
  3. To cover relevant applications in science and engineering to illustrate the utility of learning these topics
  4. To use mathematical software, in problem solving, to allow the solution of more complex problems and provide visualization of the mathematical concepts in three dimensions.

 Reading list:

  1. Anton, I. C. Bivens, S. Davis, “Calculus, Early Transcendental”, 11th edition, John Wiley, New York, 2016.
  2. Stewart, “Calculus”, 8th edition, Brooks/Cole, 2016.
  3. B. Thomas, A. R. Finney, “Calculus”, 14th edition, Pearson, USA, 2017.

 Lecture-wise distribution of the Contents

Lecture #

Topic

L1

Introduction to the course

L2-L3

3-Dimensional Coordinate Systems and Vectors.

L4

Dot Product.

L5

Cross Product.

L6

Lines and Planes in Space.

L7-L8

Cylinders and Quadric Surfaces

L9-L10

Curves and Tangents in Space.

L11-L12

Integrals of Vector Functions: Projectile Motion.

L13

Arc Length of Space Curves.

L14-L15

Functions of Several Variables.

L16

Partial Derivatives.

L17

The Chain Rule.

L18-L19

Directional Derivatives and Gradients.

L20-L21

Tangent Planes and Differentials.

L22

MID EXAM

L22-L23

Extrema and Saddle Points.

L24

Lagrange Multipliers.

L25-L26

Double and Iterated Integrals over Rectangles.

L27

Double Integrals over General Regions.

L28

Double Integrals in Polar Form.

L29-L30

Triple Integrals in Rectangular Coordinates.

L31-L32

Triple Integrals in Cylindrical Coordinates.

L33-L34

Line Integrals.

L35-L37

Vector Fields and Line Integrals: Work, Circulation and Flux.

L38-L40

Path Independence, Conservative Fields and Potential Functions.

L41-L42

Green’s Theorem in the plane.

L43-L44

Surface Area and Surface Integrals.

L45-L46

Divergence Theorem.

L47-L48

Stoke’s Theorem.

Course Code:    MATH241

Course Title:                  Mathematical Statistics-I

Credit Hours:                 (3 0 3)

Pre-requisite(s):            MATH101

 Course Objectives:

  1. To learn how to handle data numerically and graphically
  2. To understand the basic principles of random variables and random processes needed in applications
  3. To learn discrete random variables and their probability distributions

 Reading List:

  1. S. Mann, “Introductory Statistics”, 9th edition, John Wiley & Sons, 2016.
  2. T. Craig, J. McKean, R.V. Hogg, “Introduction to Mathematical Statistics”, 7th edition, Pearson Education, 2013.
  3. R. Sheldo, “Introductory Statistics”, 3rd edition, Oxford, 2010.
  4. R. Spiegel, J.L. Schiller, R.L. Sirinivasan, “Probability and Statistics”, 2nd edition, McGraw Hill. NY, 2000.
  5. M. Clark, and D. Cooke, “A Basic Course in Statistics” 4th edition, Arnold, London, 1998.
  6. T. Mclave, P.G. Benson,T. Snitch, “Statistics for Business & Economics” 9th edition, Prentice Hall, New Jersey, 2005.
  7. M. Chaudhry, S. Kamal, “Introduction to Statistical Theory” Parts I 6th edition, Ilmi Kitab Khana, Lahore, Pakistan, 1996.

 Lecture-wise distribution of the Contents

Lecture #

Topic

L1

Review of Mathematical Statistics

L2-L4

The nature and scope of the statistics,

L5-L7

Organizing of data, classification of data and graphs,

L8- L10

Measures of central tendency: their properties, usage, limitations and comparison.

L11-L13

Continued…

L14-L16

Measures of dispersion: their properties, usage, limitations and comparison.

L17-L19

Continued…

L20-L22

Calculations for the ungrouped and grouped data, measures of skewness,

Kurtosis and distribution shapes.

L23

Mid Exam

L24-L25

Sets, probability concepts, permutation and combination.

L26-L28

Addition and multiplication rules, bivariate frequency tables, joint and marginal probabilities.

L29-L31

Conditional probability and independence, Bayes’ rule.

L32-L34

Random variables, properties of random variables, discrete and continuous

random variables

L35-L37

Percentile for continuous random variables, multivariate distributions, marginal distributions, conditional distributions.

L38-L40

Mathematical expectation, moments, Chebyshev’s theorem, moment generating

Functions

L41-L43

Relation between moments and cumulants, product moments, characteristic

Function, conditional expectations.

L44-L46

Probability distribution, discrete probability distributions, Bernoulli distribution, properties, binomial distribution,

L47-L48

Poisson and hypergeometric distributions, negative binomial and geometric

Distributions.

 Course Code: MATH202

Course Title:               Number theory

Credit Hours:              (3 0 3)

Pre-requisite(s):        None

 Course Objectives:

The objectives of this course are:

  1. To learn about divisibility and its properties.
  2. To learn about Congruencies its properties and applications.
  3. To understand Primitive Roots and Quadratic Residue.                              

Reading list:

  1. W. Stein,” Elementary Number Theory”, Springer-Verlag,2017
  2. K.H Rosen, “Elementary Number Theory and its Applications”, 6th edition, Pearson, 2010.
  3. T. Koshy, “Elementary Number Theory with Applications”, 2nd edition, Academic Press, 2007.
  4. D.M. Burton, “Elementary Number Theory”, 7th edition, McGraw-Hill, 2010.

Lecture-wise distribution of the Contents

Lecture #

Topic

L1-L3

Introduction to the course, Well-ordering  principle , Mathematical induction  Divisibility ,Transitivity of divisibility ,Division of linear combination of integers and other related properties of divisibility  

L3-L4

The Division Algorithm, Proof and consequences of Division Algorithm   

L5-L6

Representation of integers in different base systems. Arithmetic in non-decimal systems.  Negative bases 

L7-L9

Prime Numbers, Prime divisors, infinitude of primes, Upper bound for a prime factor of composite integers, Sieve of Eratosthenes , Prime number theorem(without proof)

L10-L12

Greatest Common Divisor, Properties of GCD(theorems) ,GCD of more than two integers , The Euclidean Algorithm for finding GCD,

L13-L15

Fibonacci numbers, GCD of successive Fibonacci numbers , Lame’s Theorem The Fundamental Theorem of Arithmetic, Least common multiple, Theorem relating GCD and LCM 

L16-L18

Fermat factorization, Fermat number, Prime divisors of Fermat number

L19-L21

Linear Diophantine Equation, Solution in integers for Linear Diophantine Equation and its Applications.

L22-L24

Congruencies, equivalence relation and partition classes, Congruencies as equivalence relation. Complete system of residues modulo m, A reduced residue system modulo m

L25

MID EXAM

L26-L28

Linear Congruencies, Criterion for existence of solution and method of solution for linear congruencies, System of linear congruencies in one variable , Chinese Reminder theorem .

L29-L31

System of linear congruencies in two or more than two  variables ,Matrix method for solution of the system ,Applications of congruencies , Divisibility Tests, The Perpetual Calendar and Hashing Functions       

L32-L33

Wilson's Theorem and Fermat's Little Theorem, Pseudo-prim, Euler phi-function ,Euler Theorem

L34-L36

Arithmetic function, Multiplicative functions, Euler phi-function as Multiplicative function , Mobius function, Mobius inversion formula

L37-L38

Functions for The Sum and Number of Divisors, Perfect Numbers and Mersenne Primes

L39-L41

Order of an Integer and primitive Roots, Incongruent Primitive roots of a positive integer ,Primitive roots for Primes

L42-L43

Lagrange's Theorem, The Existence of Primitive Roots

L44-L45

Index Arithmetic ,Quadratic Residue, Legendre symbol

L46-L48

Euler's criterion, Gauss Lemma, law of quadratic reciprocity , Jacobi symbol

 

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