Unit 1
Real analysis
Limits, continuity and convergence made rigorous.
Advanced Mathematics · University & competition
Analysis & Discrete Mathematics
Limits and rigour, sequences and series, logic, sets, graphs and combinatorics.
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What you will be able to do
- Write epsilon–delta arguments
- Test sequences and series for convergence
- Use formal logic and proof techniques
- Apply graph theory and counting arguments
Course contents
Every topic, lesson by lesson.
Unit 2
Discrete mathematics
Logic, proof, sets, combinatorics and graphs.
Unit 3
Convergence of sequences and series
Limits, the epsilon definition and standard convergence tests.
Unit 4
Graph theory
Degrees, paths, trees and shortest-path algorithms.
Concepts to practise again
Built from your saved practice attempts in this course, weakest question types first.
Complete a practice set in any lesson to see which question types to practise again.
Curriculum alignment
This course satisfies the following education systems.
American Curriculum
British Curriculum
Canadian Curriculum
Australian Curriculum