# MTH621 Handouts pdf | Real Analysis I Notes (pdf)

## MTH621: Real Analysis I

The Real Analysis I is the 1st course towards the rigorous (formal) treatment of the fundamental concepts of mathematical analysis. MTH621 Handouts pdf

# MTH621 Handouts pdf

Course Category: Mathematics

#### Course Outline

The Real Number System: Set-theoretic statements, the real and complex number systems, the principle of mathematical induction, and ordered sets.
Sequences and Series: convergent or divergent sequences and series, Some Special Sequences, Subsequence, Tests for convergent or divergent sequences and series.
Limits, Continuity and Differentiability: Limit of a function, prove various theorems about limits, sequences, and functions. Continuity of real-valued functions, prove various theorems about continuous functions with an emphasis on the proofs. Derivative of a function, proof of various theorems about dif-
differentiability of the function. Bolzano-Weierstrass theorem, Mean value theorem.
Riemann Integration:   Riemann sums,  Riemann integral, proof of various results about the Riemann integrals. MTH621 Handouts pdf

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## MTH621: Real Analysis I

#### Universal Set

The understanding that the members of all sets under consideration in any given context come from a specific collection of elements, is called the universal set.

#### Number Theory

Number theory is a branch of mathematics that studies the properties of, and the relationships between, particular types of numbers.

• The set of natural numbers N.
• The prime numbers.

The primes are the building blocks of the positive integers.