Mathematical Thinking (MATH-112 Spring 2018)

The aim of the course is to provide an introduction to fundamental skills and ideas for students who require some mathematics in their degree. The major aim of the course is not to introduce the students with the procedural mathematics but to expose them to the skills that the professional mathematicians use to solve the real world problems. In simple words the this is an attempt to develop the valuable skills of thinking outside the box. We will explore a variety of interesting ideas from diverse areas of applied mathematics

Introduction to Philosphy

This is an introductory course on philosophy.

Theory of Probably

The course covers the basic principles of the theory of probability and its applications. Topics include combinatorial analysis used in computing probabilities, the axioms of probability, conditional probability and independence of events; discrete and continuous random variables; joint, marginal, and conditional densities, moment generating function; laws of large numbers; Central limit Theorem, binomial, Poisson, gamma, univariate, and bivariate normal distributions, probability spaces, sigma-fields, probability measure and measure theoretic introduction to probability, different modes of convergence

Abstract Algebra

This is an introductory course on Algebra. The students will learn about Groups, Rings and Modules in detail. Moreover a short amount of time will be spent on covering Representation theory of finite groups.

Linear Algebra

In this course the students will learn about system of linear equations and their applications in real world problems. The whole course will primarily focus on finding solutions of systems of linear equations.  Along the way students will also learn key concepts such as echelon form and reduced echelon form, matrices and their properties, inverse of matrices, factorization of matrices, linear transformations, vector spaces and their subspaces, eigenvalues and eigenvectors for real matrices and inner product spaces.

Computing Tools For Mathematics (MATH-222, Spring-2018)

This course provides an introduction to basic computer programming concepts and techniques useful for Computer Scientists, Mathematicians and Engineers. The course exposes students to practical applications and complexities in computing and commonly used tools within these domains. It introduces techniques for problem solving, program design and algorithm development using MATLAB and/or PYTHON programming language. The content of this course gives an introduction to the MATLAB and/or PYTHON environment and the help system, data types and scalar variables, arithmetic and mathematical functions, input and output, selection and iteration statements. Functions: user defined functions, function files, passing information to and from functions, function design and program decomposition, recursion. Arrays: vectors, arrays and matrices, array addressing, vector, matrix and element-by-element operations. Graphics: 2-D and 3-D plotting. Mathematical modelling: dynamical systems, linear systems of equations, numerical differentiation and integration.

Measure Theory (MATHS-467, Spring 2018)

The modern notion of measure, developed in the late 19th century, is an extension of the notions of length, area or volume. A measure m is a law which assigns a number $m(A)$  to certain subsets A of a given space and is a natural generalization of the following notions: 1) length of an interval, 2) area of a plane figure, 3) volume of a solid, 4) amount of mass contained in a region, 5) probability that an event from A occurs, etc.

It originated in the real analysis and is used now in many areas of mathematics like, for instance, geometry, probability theory, dynamical systems, functional analysis, etc.

Given a measure m, one can define the integral of suitable real valued functions with respect to m. Riemann integral is applied to continuous functions or functions with few points of discontinuity. For measurable functions that can be discontinuous almost everywhere'' Riemann integral does not make sense. However it is possible to define more flexible and powerful Lebesgue's integral (integral with respect to Lebesgue's measure) which is one of the key notions of modern analysis.

The course will cover the following topics: Definition of a measurable space and $\sigma$-additive measures, Construction of a measure form outer measure, Construction of Lebesgue's measure, Lebesgue-Stieltjes measures, Examples of non-measurable sets, Measurable Functions, Integral with respect to a measure, Lusin's Theorem, Egoroff's Theorem, Fatou's Lemma, Monotone Convergence Theorem, Dominated Convergence Theorem, Product Measures and Fubini's Theorem. Selection of advanced topics such as Radon-Nikodym theorem, covering theorems, differentiability of monotone functions almost everywhere, descriptive definition of the Lebesgue integral, description of Riemann integrable functions, k-dimensional measures in n-dimensional spaces, divergence theorem, Riesz representation theorem, etc.

Real Analysis (Math-221 Spring 2018)

Much of mathematics relies on our ability to be able to solve equations, if not in explicit exact forms, then at least in being able to establish the existence of solutions. To do this requires a knowledge of so-called "analysis", which in many respects is just Calculus in very general settings. The foundations for this work are commenced in Real Analysis, a course that develops this basic material in a systematic and rigorous manner in the context of real-valued functions of a real variable. Topics covered are: Basic set theory. The real numbers and their basic properties. Sequences: convergence, sub-sequences, Cauchy sequences. Open, closed, and compact sets of real numbers. Continuous functions and uniform continuity. The Riemann integral. Differentiation and Mean Value theorems. The Fundamental Theorem of Calculus. Series. Power series and Taylor series. Convergence of sequences and series of functions.

Introduction to Topology (Math-222, Spring-2018)

This one-semester three-credit course in Introductory Topology will have three general interconnected objectives.
First, as it has become increasingly apparent that topology is one of the major branches of modern mathematics, this course will provide a firm foundation in topology to enable the student to continue more advanced study in this area. Second, as several important areas of mathematics, in particular modern analysis, depend upon or are clarified by the certain topics in topology, this course will present and emphasize those topics in order to aid the student in his future mathematical studies. Finally, this course hopes to expose the students to both mathematical rigor and abstraction, giving there an opportunity further to develop his mathematical maturity. The key course contents are, topological spaces; separation axioms; continuity, convergence, connectedness, and compactness; basic notions in Homotopy theory; quotient spaces; and Paracompactness, applications of Topology