1
Stage 1
Discrete Mathematics
The mathematical foundation of computer science.
Key Topics
Logic and proofsSets and functionsCombinatoricsGraph theoryRecurrence relationsGenerating functions
3 books
~10 weeks
CS & Cryptography
The math behind secure computation
Advanced
5 stages
~44 weeks
11 books
Mathematical foundations for computer science, algorithms, and cryptographic systems.
Prerequisites: Complete the foundations path first.
Skill Tree
Visualize your learning journey. Click on any stage (branch) to see the recommended books for that subject. Topics are shown as leaves on each branch.
Loading skill tree...
Learning Stages
This path is divided into 5 stages covering 27 topics. Work through each stage in order for the best learning experience.
Recommended Books for Stage 1
Discrete Mathematics and Its Applications
Rosen
Intermediate
Discrete and Combinatorial Mathematics
Grimaldi
Intermediate
Concrete Mathematics
Graham, Knuth & Patashnik
Advanced
2
Stage 2
Number Theory for Crypto
Number theory essential for cryptographic algorithms.
Key Topics
Modular arithmeticEuclidean algorithmChinese remainder theoremFermat and Euler theoremsPrimality testingFactorization
2 books
~8 weeks
Recommended Books for Stage 2
.jpg&w=3840&q=75)
Elementary Number Theory
Underwood Dudley
Intermediate
.jpg&w=3840&q=75)
Number Theory
George Andrews
Intermediate
3
Stage 3
Abstract Algebra for Crypto
Algebraic structures used in modern cryptography.
Key Topics
Group theoryFinite fieldsElliptic curvesRing theory basics
3 books
~12 weeks
Recommended Books for Stage 3
.jpg&w=3840&q=75)
Abstract Algebra: A First Course
Dan Saracino
Beginner
.jpg&w=3840&q=75)
Contemporary Abstract Algebra
Joseph Gallian
Intermediate
.jpg&w=3840&q=75)
Algebra
Michael Artin
Advanced
4
Stage 4
Probability for CS
Probabilistic methods in algorithms and security.
Key Topics
Discrete probabilityRandom variablesExpectationRandomized algorithmsInformation theory
2 books
~6 weeks
Recommended Books for Stage 4
A First Course in Probability
Sheldon Ross
Intermediate
Schaum's Outline of Probability and Statistics
Schaum's
Intermediate
5
Stage 5
Cryptography
Modern cryptographic theory and practice.
Key Topics
Symmetric encryptionPublic key cryptographyHash functionsDigital signaturesZero-knowledge proofsCryptographic protocols
1 book
~8 weeks
Recommended Books for Stage 5
Cryptography: Theory and Practice
Stinson
Advanced
All Books in This Path
Complete list of 11 recommended books across all stages. You don't need to buy them all — pick what works for you.
Discrete Mathematics and Its Applications
by Rosen
Widely used in US discrete math courses. Tough read but solid content.
Discrete and Combinatorial Mathematics
by Grimaldi
Standard discrete math book. Takes effort but solid fundamentals.
Concrete Mathematics
by Graham, Knuth & Patashnik
Legendary book by famous computer scientists including Knuth (creator of TeX). Has answers to all problems. More advanced.
Elementary Number Theory
by Underwood Dudley
Had this one the longest. Great book, smells wonderful! Classic number theory text.
Number Theory
by George Andrews
Excellent choice for learning number theory. Any of these books will work.
Abstract Algebra: A First Course
by Dan Saracino
Easier than Fraleigh and Gallian. Better for true beginners in abstract algebra.
Contemporary Abstract Algebra
by Joseph Gallian
The book of examples! Has many examples not found in other abstract algebra books.
Algebra
by Michael Artin
Classic graduate-level book. Heavy linear algebra focus. Great examples and exercises.
A First Course in Probability
by Sheldon Ross
Nice thin book with fantastic examples. Some calculus required (triple integrals).
Schaum's Outline of Probability and Statistics
by Schaum's
Very affordable. Tons of examples in both probability and statistics. Good supplement.
Cryptography: Theory and Practice
by Stinson
Almost read 100% through. Used for grad school course. Lots of algorithms and math.
What's Next?
Complete this path and continue your mathematical journey.