**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-

**Riemann Integration:**Riemann sums, Riemann integral, proof of various results about the Riemann integrals. MTH621 Handouts pdf

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### MTH621 HANDOUTS

**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.