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SMA 300 Mathematics

SMA 300 • Real Analysis I

Canonical syllabus units, structured theorems, lecture notes, and past examination problems.

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Syllabus Units

Curriculum outline, core theorems, and revision problems.
6 Topics
Unit 01

The Real Number System

This foundational module outlines the structural architecture of real numbers, comparing rational and irrational numbers, and establishing the properties of bounds and completeness

Field and Order Structure Rational and Irrational Numbers Intervals Bounded Sets Supremum and Infimum Completeness Axiom Density of Rational Numbers
36 Verified Questions Study Topic →
Unit 02

Topology of the Real Numbers

This module covers the spatial relationships and structural classifications of point sets within the real line

Neighborhoods Interior Points and Open Sets Limit Points and Derived Sets Closed Sets and Closure Dense Sets
22 Verified Questions Study Topic →
Unit 03

Sequences

This module details how ordered lists of numbers behave as they progress toward infinity

Convergence of Sequences Properties of Sequences Subsequences Cauchy Sequences Monotonic Sequences Limit Superior and Limit Inferior
10 Verified Questions Study Topic →
Unit 04

Series

This module shifts from sequences to infinite series, looking at the summation of infinitely many terms and evaluating whether the total sum is finite

Introduction to Infinite Series Special Series Rules nth Term Divergence Test Convergence Tests Absolute vs. Conditional Convergence
18 Verified Questions Study Topic →
Unit 06

Functions

The final module applies the rigorous topological and sequential properties established in prior modules directly to real-valued functions

Limits of Functions Pointwise Continuity Uniform Continuity
4 Verified Questions Study Topic →