BS Math 3rd Semester
BS Mathematics (Semester Plan)
The BS Mathematics degree program is divided into eight semesters as follows.
Code 
Course Title 
CrHr 
PreReq 

Code 
Course Title 
CrHr 
PreReq 

Year 1 Semester 1 

Year 1 Semester II 

XXX*** 
URI 
4(3+1) 
None 

MATH102 
CalculusII 
3(3+0) 
MATH101 

MATH101 
CalculusI 
3(3+0) 
None 

MATH103 
Discrete Mathematics 
3(3+0) 
None 

XXX*** 
URII 
3(3+0) 
None 

XXX*** 
URIV 
3(3+0) 
None 

XXX*** 
URIII 
3(3+0) 
None 

XXX*** 
URV 
3(3+0) 
None 

XXX*** 
FRI 
3(3+1) 
None 

XXX*** 
FRII 
4(3+1) 
None 

Year 2 Semester III 

Year 2 Semester IV 

MATH201 
CalculusIII 
3(3+0) 
MATH102 

MATH211 
Group Theory 
3(3+0) 
None 

XXX*** 
FRIII 
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*** 
FRIV 
3(3+0) 
None 

XXX*** 
FRV 
3(3+0) 
None 

XXX*** 
URVI 
3(3+0) 
None 

XXX*** 
FRVI 
3(3+0) 
None 

XXX*** 
URVII 
3(3+0) 
None 

XXX*** 
FRVII 
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 AnalysisI 
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 
ElectiveII 
3(3+0)/4(3+1) 
MATHxxx 

MATH313 
Rings & Fields 
3(3+0) 
MATH211 

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

MATHxxx 
ElectiveI 
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 AnalysisII 
4(3+1) 
MATH331 

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

MATHXXX/ 
Elective/Report Writing & Presentation 
3(3+0)/4(3+1) 
MATHxxx 

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


Elective/Senior Design ProjectI 
3(0+9)/3(3+0)/4(3+1) 
MATHxxx 


Elective/Senior Design ProjectII 
3(0+9)/3(3+0)/ 4(3+1) 
MATHxxx 

Note: UR: University Requirement Courses, FR: Faculty Requirement Courses
Course Code: MATH201
Course Title: CalculusIII
Credit Hours: (3 0 3)
Prerequisite(s): MATH102
Course Objectives:
The objectives of this course are:
 To apply previously developed skills learned in Calculus to learn Multivariable Calculus and Vectors
 To cover Vectors, Partial Derivatives, Multiple Integrals and Vector Fields in order to prepare students for further study in technological disciplines.
 To cover relevant applications in science and engineering to illustrate the utility of learning these topics
 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:
 Anton, I. C. Bivens, S. Davis, “Calculus, Early Transcendental”, 11^{th} edition, John Wiley, New York, 2016.
 Stewart, “Calculus”, 8^{th} edition, Brooks/Cole, 2016.
 B. Thomas, A. R. Finney, “Calculus”, 14^{th} edition, Pearson, USA, 2017.
Lecturewise distribution of the Contents
Lecture # 
Topic 
L1 
Introduction to the course 
L2L3 
3Dimensional Coordinate Systems and Vectors. 
L4 
Dot Product. 
L5 
Cross Product. 
L6 
Lines and Planes in Space. 
L7L8 
Cylinders and Quadric Surfaces 
L9L10 
Curves and Tangents in Space. 
L11L12 
Integrals of Vector Functions: Projectile Motion. 
L13 
Arc Length of Space Curves. 
L14L15 
Functions of Several Variables. 
L16 
Partial Derivatives. 
L17 
The Chain Rule. 
L18L19 
Directional Derivatives and Gradients. 
L20L21 
Tangent Planes and Differentials. 
L22 
MID EXAM 
L22L23 
Extrema and Saddle Points. 
L24 
Lagrange Multipliers. 
L25L26 
Double and Iterated Integrals over Rectangles. 
L27 
Double Integrals over General Regions. 
L28 
Double Integrals in Polar Form. 
L29L30 
Triple Integrals in Rectangular Coordinates. 
L31L32 
Triple Integrals in Cylindrical Coordinates. 
L33L34 
Line Integrals. 
L35L37 
Vector Fields and Line Integrals: Work, Circulation and Flux. 
L38L40 
Path Independence, Conservative Fields and Potential Functions. 
L41L42 
Green’s Theorem in the plane. 
L43L44 
Surface Area and Surface Integrals. 
L45L46 
Divergence Theorem. 
L47L48 
Stoke’s Theorem. 
Course Code: MATH241
Course Title: Mathematical StatisticsI
Credit Hours: (3 0 3)
Prerequisite(s): MATH101
Course Objectives:
 To learn how to handle data numerically and graphically
 To understand the basic principles of random variables and random processes needed in applications
 To learn discrete random variables and their probability distributions
Reading List:
 S. Mann, “Introductory Statistics”, 9^{th} edition, John Wiley & Sons, 2016.
 T. Craig, J. McKean, R.V. Hogg, “Introduction to Mathematical Statistics”, 7^{th} edition, Pearson Education, 2013.
 R. Sheldo, “Introductory Statistics”, 3^{rd} edition, Oxford, 2010.
 R. Spiegel, J.L. Schiller, R.L. Sirinivasan, “Probability and Statistics”, 2^{nd} edition, McGraw Hill. NY, 2000.
 M. Clark, and D. Cooke, “A Basic Course in Statistics” 4^{th} edition, Arnold, London, 1998.
 T. Mclave, P.G. Benson,T. Snitch, “Statistics for Business & Economics” 9th edition, Prentice Hall, New Jersey, 2005.
 M. Chaudhry, S. Kamal, “Introduction to Statistical Theory” Parts I 6^{th} edition, Ilmi Kitab Khana, Lahore, Pakistan, 1996.
Lecturewise distribution of the Contents
Lecture # 
Topic 
L1 
Review of Mathematical Statistics 
L2L4 
The nature and scope of the statistics, 
L5L7 
Organizing of data, classification of data and graphs, 
L8 L10 
Measures of central tendency: their properties, usage, limitations and comparison. 
L11L13 
Continued… 
L14L16 
Measures of dispersion: their properties, usage, limitations and comparison. 
L17L19 
Continued… 
L20L22 
Calculations for the ungrouped and grouped data, measures of skewness, Kurtosis and distribution shapes. 
L23 
Mid Exam 
L24L25 
Sets, probability concepts, permutation and combination. 
L26L28 
Addition and multiplication rules, bivariate frequency tables, joint and marginal probabilities. 
L29L31 
Conditional probability and independence, Bayes’ rule. 
L32L34 
Random variables, properties of random variables, discrete and continuous random variables 
L35L37 
Percentile for continuous random variables, multivariate distributions, marginal distributions, conditional distributions. 
L38L40 
Mathematical expectation, moments, Chebyshev’s theorem, moment generating Functions 
L41L43 
Relation between moments and cumulants, product moments, characteristic Function, conditional expectations. 
L44L46 
Probability distribution, discrete probability distributions, Bernoulli distribution, properties, binomial distribution, 
L47L48 
Poisson and hypergeometric distributions, negative binomial and geometric Distributions. 
Course Code: MATH202
Course Title: Number theory
Credit Hours: (3 0 3)
Prerequisite(s): None
Course Objectives:
The objectives of this course are:
 To learn about divisibility and its properties.
 To learn about Congruencies its properties and applications.
 To understand Primitive Roots and Quadratic Residue.
Reading list:
 W. Stein,” Elementary Number Theory”, SpringerVerlag,2017
 K.H Rosen, “Elementary Number Theory and its Applications”, 6th edition, Pearson, 2010.
 T. Koshy, “Elementary Number Theory with Applications”, 2^{nd} edition, Academic Press, 2007.
 D.M. Burton, “Elementary Number Theory”, 7^{th} edition, McGrawHill, 2010.
Lecturewise distribution of the Contents
Lecture # 
Topic 
L1L3 
Introduction to the course, Wellordering principle , Mathematical induction Divisibility ,Transitivity of divisibility ,Division of linear combination of integers and other related properties of divisibility 
L3L4 
The Division Algorithm, Proof and consequences of Division Algorithm 
L5L6 
Representation of integers in different base systems. Arithmetic in nondecimal systems. Negative bases 
L7L9 
Prime Numbers, Prime divisors, infinitude of primes, Upper bound for a prime factor of composite integers, Sieve of Eratosthenes , Prime number theorem(without proof) 
L10L12 
Greatest Common Divisor, Properties of GCD(theorems) ,GCD of more than two integers , The Euclidean Algorithm for finding GCD, 
L13L15 
Fibonacci numbers, GCD of successive Fibonacci numbers , Lame’s Theorem The Fundamental Theorem of Arithmetic, Least common multiple, Theorem relating GCD and LCM 
L16L18 
Fermat factorization, Fermat number, Prime divisors of Fermat number 
L19L21 
Linear Diophantine Equation, Solution in integers for Linear Diophantine Equation and its Applications. 
L22L24 
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 
L26L28 
Linear Congruencies, Criterion for existence of solution and method of solution for linear congruencies, System of linear congruencies in one variable , Chinese Reminder theorem . 
L29L31 
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 
L32L33 
Wilson's Theorem and Fermat's Little Theorem, Pseudoprim, Euler phifunction ,Euler Theorem 
L34L36 
Arithmetic function, Multiplicative functions, Euler phifunction as Multiplicative function , Mobius function, Mobius inversion formula 
L37L38 
Functions for The Sum and Number of Divisors, Perfect Numbers and Mersenne Primes 
L39L41 
Order of an Integer and primitive Roots, Incongruent Primitive roots of a positive integer ,Primitive roots for Primes 
L42L43 
Lagrange's Theorem, The Existence of Primitive Roots 
L44L45 
Index Arithmetic ,Quadratic Residue, Legendre symbol 
L46L48 
Euler's criterion, Gauss Lemma, law of quadratic reciprocity , Jacobi symbol 