Learning Resources
This module is populated from the local chunked books in library/raw/semester-01-math-foundations/books. Use this page as a source map, not as a reading dump.
Source Stack
| Book | Role | How to use it in this module |
|---|---|---|
| Mathematics for Computer Science | Primary teaching source | Default escalation for proof templates, logic, sets, functions, and induction |
| Discrete Mathematics and Its Applications | Selective support and exercise source | Use when you need extra examples, alternate wording, or more exercise volume |
| Elementary Number Theory | Not used directly here | Save for later number-theory-heavy work |
| Introduction to Probability | Not used directly here | Save for Module 3 |
| Linear Algebra and Its Applications | Not used directly here | Save for Module 4 |
| How To Solve It By Computers | Not used directly here | Save for Module 5 problem-solving work |
Resource Map by Cluster
Cluster 1: Logical Language
| Need | Best local chunk | Why |
|---|---|---|
| proposition shape and implication | MCS 3.1 | Fastest entry into compound statements |
| equivalence and validity | MCS 3.3 | Best support for truth-table reasoning |
| quantified statements | MCS 3.6 | Clean bridge from predicates to full claims |
| alternate explanation of quantifiers | Rosen 1.4 | Good second pass when scope or negation is shaky |
Cluster 2: Proof Construction
| Need | Best local chunk | Why |
|---|---|---|
| direct implication proofs | MCS 1.5 | Gives usable proof templates |
iff, cases, contradiction | MCS 1.6 | Best chunk for proof-form comparison |
| proof style and readability | MCS 1.9 | Best source for turning scratchwork into readable proofs |
| extra proof volume | Rosen 1.7 | More examples and exercise-style statements |
Cluster 3: Sets and Functions
| Need | Best local chunk | Why |
|---|---|---|
| membership, subsets, power sets | MCS 4.1 | Most concise source for set language |
| set logic and identities | MCS 8.3 | Good deepening source for set algebra |
| domain, codomain, image, range | MCS 4.3 | Strong conceptual treatment of functions |
| more function examples | Rosen 2.3 | Helpful for injective and surjective classification practice |
Cluster 4: Relations and Order
| Need | Best local chunk | Why |
|---|---|---|
| relation property tests | Rosen 9.1 | Dense with examples and counterexamples |
| equivalence relations | Rosen 9.5 | Best focused treatment of class formation |
| partial orders | Rosen 9.6 | Strong on comparability and order structure |
| partial-order intuition | MCS 10.7 | Good CS-flavored perspective |
Cluster 5: Induction and Recursion
| Need | Best local chunk | Why |
|---|---|---|
| ordinary induction template | MCS 5.1 | Best step-by-step structure |
| strong induction and minimal counterexample thinking | MCS 5.2-5.3 | Best bridge between forms of induction |
| recursive objects and structural induction | MCS 7.1 | Directly connects recursive construction to proof |
| alternate induction source | Rosen 5.1-5.3 | Good for extra practice volume |
Exercise Support Chunks
Use these when the concept pages are understood but your speed or fluency is weak:
- MCS: What is a Proof? Problems and References
- MCS: Logical Formulas Problems and References
- MCS: Directed Graphs & Partial Orders Problems and References
- Rosen: Answers to Odd-Numbered Exercises
Use Rules
- If you are stuck on proof setup, go to
MCSfirst. - If you want more raw exercise volume, go to
Rosen. - If you only need one clarification, open one chunk, not an entire chapter sequence.
- If you are rereading the same chunk repeatedly, stop and rewrite the concept in your own words before reading more.