An investigation into the mathematical foundations of calculus. Through lectures and exercises, visit fundamental concepts of mathematical analysis including logic, basic set theory, functions, number systems, order completeness of the real numbers and its consequences, sequences and series, topology of R^n, continuous functions, uniform convergence, compactness, and theory of differentiation and integration. Expand mathematical proof and writing skills through ample practice with LaTex to communicate mathematics effectively and demonstrate rigorous math thinking in preparation for more advanced courses.

Basic Set Theory and Mathematical Logic

Definition and properties of Fields

Real number system

Fundamental Property of real numbers

Sequence and Limits

Properties of limits, bounded and monotone sequences

Bolzano-Weierstrass Theorem and Cauchy sequence

Series and convergence test

Basic topology of real line and limits of functions

Limits and continuity of functions

Continuous function on compact interval and uniform continuity

Derivatives and Mean Value Property

Riemann Integral and Fundamental Theorem of Calculus

Metric spaces introduction

Exam 1 : 30% , Exam 2: 30%, Homework: 40%

Introduction to Real Analysis, Robert G. Bartle and Donald R. Sherbert, 4th edition.

Principles of Mathematical Analysis, Rudin, 3rd edition.

Alternate years course, AY2024