Core Math
Mathematics forms the theoretical foundation for computer science. Discrete math is particularly important and closely related to the study of algorithms and data structures. Calculus helps develop mathematical maturity and prepares students for discrete math.
Topics Covered
- Discrete mathematics
- Mathematical proofs
- Basic statistics
- O-notation
- Discrete probability
- Differential calculus
- Integral calculus
- Coordinate systems
- Infinite series
- And more
Course Sequence
| Course | Duration | Effort | Prerequisites | Notes |
|---|---|---|---|---|
| Calculus 1A: Differentiation | 13 weeks | 6-10 hours/week | High school math | Alternative: MIT OCW Single Variable Calculus covers all 3 calculus courses |
| Calculus 1B: Integration | 13 weeks | 5-10 hours/week | Calculus 1A | |
| Calculus 1C: Coordinate Systems & Infinite Series | 6 weeks | 5-10 hours/week | Calculus 1B | |
| Mathematics for Computer Science | 13 weeks | 5 hours/week | Calculus 1C | Alternative: OCW Mathematics for Computer Science |
Why These Courses?
This sequence is designed to build your mathematical foundation from the ground up:
- Calculus teaches you the language of continuous mathematics and builds problem-solving skills
- Mathematics for Computer Science focuses on discrete math, which is directly applicable to algorithms, data structures, and theoretical computer science
Learning Outcomes
After completing the Core Math sequence, you will:
- Understand mathematical reasoning and proof techniques
- Apply calculus concepts to solving problems
- Work with discrete mathematical structures
- Analyze algorithm complexity using O-notation
- Apply probability theory to computational problems
- Have the mathematical foundation needed for advanced CS topics
Importance for Computer Science
Mathematics is central to computer science in many ways:
- Algorithm Analysis - Uses mathematical techniques to predict resource usage
- Cryptography - Based on number theory and abstract algebra
- Machine Learning - Relies heavily on statistics, linear algebra, and calculus
- Graphics - Uses geometry and linear algebra
- Formal Verification - Uses logic and proof techniques
Building a strong mathematical foundation now will make many advanced CS topics much more accessible later.