HIGH-YIELD REVISION GUIDE & CHEAT SHEET
Discrete Mathematics & Probability
Complete Semester Guide
High-Yield Comprehensive Guide, Formal Proofs, RSA Step-by-Step Hand
Calculations, Planar Graphs & Quick-Cram Appendix
Computer Science & Theoretical Mathematics | Course Code: University Of California -
Berkeley - CS 70 | 2024-2025 Comprehensive Edition
📘 WHAT’S INSIDE THIS GUIDE:
✔ Mathematical Proof Rigor: Direct proof, contradiction templates (irrationality of sqrt(2)), and
Simple vs. Strong Induction
✔ Modular Arithmetic & Number Theory: Bézout's Identity, Extended Euclidean algorithm, and
Fermat's Little Theorem exponent reduction
✔ WORKED STEP-BY-STEP PROBLEM: Full hand calculation of RSA key generation, encryption,
and decryption verification
✔ Graph Theory Core: Eulerian tour proofs (Handshaking Lemma), Planar Graph bounds (Euler's
V - E + F = 2), and Bipartite cycles
✔ Combinatorics & Counting: Stars and Bars formula with empty vs. non-empty bins and
Pigeonhole Principle
✔ Discrete Probability & Tail Bounds: Bayes' Rule, Linearity of Expectation proofs, Markov, and
Chebyshev bounds
✔ 10 Deadly CS 70 Exam Traps (Induction base cases, modular inverses, conditional indepen-
dence myths)
✔ APPENDIX: 1-Hour Emergency Pre-Exam Quick-Cram Cheat Sheet with master discrete math
theorems and 25 active recall flashcards
, Computer Science & Theoretical Mathematics · Univer-Discrete Mathematics & Probability Complete Semester
sity Of California - Berkeley - CS 70 Guide
Disclaimer: This is an independently created academic study aid. It is not affiliated with, endorsed by, or sponsored by any specific
university, textbook author, or publisher.
Independent Study Aid. Not affiliated with or endorsed by any specific university or Page 2 of 6
publisher.
Discrete Mathematics & Probability
Complete Semester Guide
High-Yield Comprehensive Guide, Formal Proofs, RSA Step-by-Step Hand
Calculations, Planar Graphs & Quick-Cram Appendix
Computer Science & Theoretical Mathematics | Course Code: University Of California -
Berkeley - CS 70 | 2024-2025 Comprehensive Edition
📘 WHAT’S INSIDE THIS GUIDE:
✔ Mathematical Proof Rigor: Direct proof, contradiction templates (irrationality of sqrt(2)), and
Simple vs. Strong Induction
✔ Modular Arithmetic & Number Theory: Bézout's Identity, Extended Euclidean algorithm, and
Fermat's Little Theorem exponent reduction
✔ WORKED STEP-BY-STEP PROBLEM: Full hand calculation of RSA key generation, encryption,
and decryption verification
✔ Graph Theory Core: Eulerian tour proofs (Handshaking Lemma), Planar Graph bounds (Euler's
V - E + F = 2), and Bipartite cycles
✔ Combinatorics & Counting: Stars and Bars formula with empty vs. non-empty bins and
Pigeonhole Principle
✔ Discrete Probability & Tail Bounds: Bayes' Rule, Linearity of Expectation proofs, Markov, and
Chebyshev bounds
✔ 10 Deadly CS 70 Exam Traps (Induction base cases, modular inverses, conditional indepen-
dence myths)
✔ APPENDIX: 1-Hour Emergency Pre-Exam Quick-Cram Cheat Sheet with master discrete math
theorems and 25 active recall flashcards
, Computer Science & Theoretical Mathematics · Univer-Discrete Mathematics & Probability Complete Semester
sity Of California - Berkeley - CS 70 Guide
Disclaimer: This is an independently created academic study aid. It is not affiliated with, endorsed by, or sponsored by any specific
university, textbook author, or publisher.
Independent Study Aid. Not affiliated with or endorsed by any specific university or Page 2 of 6
publisher.
