F.Y.B.Sc 
USMT 101 
CALCULUS I 
 Students get knowledge of fundamental principles, tools and methods in Mathematics.
 Logical thinking abilities are developed.

USMT 102 
ALGEBRA I 
 Students get knowledge of numbers and operations on numbers.
 Students know the various mathematical ideas and tools.
 Students know how to use the mathematical tools by modeling, solving and interpreting.

USMT 201 
CALCULUS II 
 Students know the various mathematical ideas and tools
 Students know how to use the mathematical tools by modeling, solving and interpreting.

USMT 202 
LINEAR ALGEBRA 
 Students know the various mathematical ideas and tools
 Students know how to use the mathematical tools by modeling, solving and interpreting.

S.Y.B.Sc. 
USMT 301 
CALCULUS III 
 Students get the broad view of the subject and develop the mathematical tools.
 Students can think in abstract manner.

USMT 302 
ALGEBRA III 
 Abstract thinking abilities are developed.
 Students know the real life applications of mathematical concepts.

USMT 303 
INTRODUCTION TO COMPUTING & PROBLEM SOLVING I 
 Students can deal with numerical problems very well.
 Numerical abilities are enhanced.

USMT 401 
CALCULUS IV 
 Students are exposed to broader mathematical concepts
 They develop the ability to use the mathematical tools for further studies of science and Mathematics.

USMT 402 
ORDINARY DIFFERENTIAL EQUATIONS 
 Students get exposed to the applied branch of Mathematics.
 They know the applications of differential equations in various other fields.

USMT 403 
INTRODUCTION TO COMPUTING & PROBLEM SOLVING II 
 Students are exposed to programming for Mathematics.
 Computer related abilities are enhanced.

T.Y.B.Sc 
USMT 501 
INTEGRAL CALCULUS 
 Problem solving skills are enhanced.
 Mathematical modeling abilities are focused.
 Abstract thinking level is uplifted.

USMT 502 
LINEAR ALGEBRA 
 Knowledge of shapes and rotations reflections is made further concrete.
 Students can relate mathematics to real life.

USMT 503 
TOPOLOGY OF METRIC SPACES 
 Logical thinking is developed.
 Problem solving skill and mathematical modeling skill are enhanced.

USMT 5C4 
GRAPH THEORY 
 Students get known to the applied branch of Mathematics.
 Many real life problems are related to graphs and can be solved using these techniques.

USACCA501 
COMPUTER PROGRAMMING AND SYSTEM ANALYSIS I 
 Improved Logical Thinking
 Enhanced programming skills

USMT 601 
REAL AND COMPLEX ANALYSIS 
 Students know new number system and their properties.
 They are exposed to new field of the subject

USMT 602 
ALGEBRA 
 Problem solving skills are enhanced.
 Students get ideas of different algebraic structures.

USMT 603 
METRIC TOPOLOGY 
 Problem solving and mathematical modeling skills are enhanced.
 Different new concepts are made familiar to the students.

USMT 6C4 
GRAPH THEORY AND COMINATORICS 
 Different counting techniques and their uses are made known to the students.
 Students get knowledge about networking.
 Students are now able to apply their knowledge of the subject into real life.

USACCA601 
COMPUTER PROGRAMMING AND SYSTEM ANALYSIS II 
 Improved Logical Thinking
 Enhanced programming skills

M.Sc – I
Semester I 
PSMT 101 
Algebra I 
 Use computational techniques and algebraic skills essential for the study of systems of linear equations, matrix algebra, vector spaces, eigenvalues and eigenvectors, orthogonality and diagonalization. (Computational and Algebraic Skills).
 Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra. (Proof and Reasoning).

PSMT 102 
Analysis I 
 Describe the real line as a complete, ordered field
 Determine the basic topological properties of subsets of the real numbers
 Use the definitions of convergence as they apply to sequences, series, and functions
 Determine the continuity, differentiability, and integrability of functions defined on subsets of the real line,Apply the Mean Value Theorem and the Fundamental Theorem of Calculus to problems in the context of real analysis
 Produce rigorous proofs of results that arise in the context of real analysis.

PSMT 103 
Complex Analysis 
 how complex numbers provide a satisfying extension of the real numbers
 Appreciate how throwing problems into a more general context may enlighten one about a specific context (e.g. solving real integrals by doing complex integration; Taylor series of a complex variable illuminating the relationship between real function that seem unrelated — e.g. exponentials and trignometric functions);
 Learn techniques of complex analysis that make practical problems easy (e.g. graphical rotation and scaling as an example of complex multiplication)

PSMT 104 
DISCRETE MATHEMATICS 
 Solve counting problems by applying elementary counting techniques using the product and sum rules, permutations, combinations, the pigeonhole principle, and binomial expansion.
 Solve discrete probability problems and use sets to solve problems in combinatorics and probability theory.
 Describe binary relations between two sets; determine if a binary relation is reflexive, symmetric, or transitive or is an equivalence relation; combine relations using set operations and composition.

PSMT 105 
Set Theory and Logic 
 Simplify and evaluate basic logic statements including compound statements, implications, inverses, converses, and contrapositives using truth tables and the properties of logic.
 Express a logic sentence in terms of predicates, quantifiers, and logical connectives
 Apply the operations of sets and use Venn diagrams to solve applied problems
 solve problems using the principle of inclusionexclusion.

M.Sc – I
Sem II 
PSMT301 
Algebra II 
The student is able to
 Demonstrate knowledge and Understanding of fundamental concepts including groups, subgroups , normal subgroups, homomorphism and isomorphism.
 Demonstrate knowledge and understanding of rings, fields and their properties.
 Apply algebraic ways of thinking
 Understand and prove fundamental results and solve algebraic problems using appropriate techniques.

PSMT202 
TOPOLOGY 
A student will be able to:
 Define and illustrate the concept of topological spaces and continuous functions.
 Define and illustrate the concept of product topology and quotient topology.
 Prove a selection of theorems concerning topological spaces, continuous functions, product topologies and quotient topologies.
 Define and illustrate the concept of the seperation axioms.
 Define connectedness and compactness and prove a selection of related theorems.

PSMT203 
ANALYSIS II 
A student will be able to:
 understand how Lebesgue measure on R is defined
 understand basic properties are measurable functions
 understand how measures may be used to construct integrals
 know the basic convergence theorems for the Lebesgue integral
 understand the relation between differentiation and Lebesgue integration.

PSMT204 
DIFFERENTIAL EQUATIONS 
A student will be able to:
 Learn how the differential equations are used to study various physical problems such as mass attached to spring and electric circuit problem etc.
 Obtain power series solutions of several important classes of ordinary differential equations including Bessel’s, Legendre, and Chebyshev’s differential equations.
 Understand the SturmLiouville problem and analyze stability of linear and nonlinear systems.
 Solve the firstorder linear differential equations.

PSMT205 
PROBABILITY THEORY 
A student will be able to
 demonstrate understanding the random variable, expectation, variance and distributions.
 explain the large sample properties of sample mean.
 understand the concept of the sampling distribution of a statistic, and in particular describe the behaviour of the sample mean
 analyse the correlated data and fit the linear regression models.
 demonstrate understanding the estimation of mean and variance and respective one sample and twosample hypothesis tests.

M.Sc II
Sem III 
PSMT301 
Algebra III 
 Demonstrate understanding of the concepts of a module and their role in mathematics.
 Demonstrate familiarity with a range of examples of these structures.
 Demonstrate familiarity with a range of examples of these structures.
 Explain the structure theorem for finitely generated modules over a principal ring and its applications to abelian groups and matrices.
 Demonstrate skills in communicating mathematics orally and in writing.

PSMT302 
Functional Analysis 
 Verify the axioms of normed vector spaces, Banach spaces and Hilbert spaces in specific examples, applying relevant tests for completeness or the existence of an inner product
 Compute the norms and spectra of (certain classes of) operators
 Use completeness arguments to produce existence proofs for operators and linear functionals with desired properties
 Establish wellknown isometric isomorphisms between sequence spaces and their dual spaces.

PSMT303 
Differential Geometry 
 The course aims to give a proper background in differential geometry for applications in theoretical physics and for further studies in geometry/geometrical analysis
 The course introduces the fundamentals of differential geometry primarily by focussing on the theory of curves and surfaces in three space. The theory of curves studies global properties of curves such as the four vertex theorem.
 The theory of surfaces introduces the fundamental quadratic forms of a surface, intrinsic and extrinsic geometry of surfaces.

PSMT304 
Numerical Analysis 
 Derive appropriate numerical methods to solve algebraic and transcendental equations
 Develop appropriate numerical methods to approximate a function
 Develop appropriate numerical methods to solve a differential equation
 Derive appropriate numerical methods to evaluate a derivative at a value
 Derive appropriate numerical methods to solve a linear system of equations
 Perform an error analysis for various numerical methods
 Prove results for various numerical root finding methods
 Derive appropriate numerical methods to calculate a definite integral
 Code various numerical methods in a modern computer language

PSMT305 
Graph Theory 
 Demonstrate knowledge of the syllabus material
 Write precise and accurate mathematical definitions of objects in graph theory
 Use mathematical definitions to identify and construct examples and to distinguish examples from nonexamples
 Validate and critically assess a mathematical proof
 Use a combination of theoretical knowledge and independent mathematical thinking in creative investigation of questions in graph theory
 Reason from definitions to construct mathematical proofs

M.Sc IV
sem IV 
PSMT401 
Field Theory 
 Explain the fundamental concepts of field extensions and Galois theory and their role in Modern mathematics
 Demonstrate accurate and efficient use of field extensions and Galois theory
 Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from field extensions and Galois theory

PSMT402 
Fourier Analysis 
 Indepth knowledge of Fourier analysis and its applications to problems in engineering.
 An ability to communicate reasoned arguments of a mathematical nature in both written and oral form.
 An ability to read and construct rigorous mathematical arguments.

PSMT403 
Calculus on Manifolds 
 The student having seen basic analysis and linear algebra is expected to learn how these topics play a significant role, first in multivariate calculus which then naturally leads to calculus on manifolds.
 The intimate relationship between analysis and geometry should become apparent at the end of this course.

PSMT404 
Linear Programming, Optimisation 
 Identify and express a decision problem in mathematical form and solve it graphically and by Simplex method
 Recognize and formulate transportation, assignment problems and drive their optimal solution
 Identify parameters that will influence the optimal solution of an LP problem and derive feasible solution using a technique of O R.
 Feasibility study for solving an optimization problem

PSMT404 
Linear Programming, Optimisation 
 Identify and express a decision problem in mathematical form and solve it graphically and by Simplex method
 Recognize and formulate transportation, assignment problems and drive their optimal solution
 Identify parameters that will influence the optimal solution of an LP problem and derive feasible solution using a technique of O R.
 Feasibility study for solving an optimization problem

PSMT405 
Project Course 
 Use mathematical ideas to model realworld problems
 Communicate mathematical ideas with others
 Utilize technology to address mathematical ideas
