1
Stage 1
Basic Algebra
Master the fundamentals of algebra that underpin all of mathematics.
Key Topics
Variables and expressionsSolving equationsInequalitiesPolynomialsFactoringRational expressions
2 books
~6 weeks
Foundations
Where every math journey begins
Beginner
4 stages
~24 weeks
10 books
Build rock-solid mathematical foundations. Perfect for those starting from scratch or filling gaps in their knowledge.
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.
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Learning Stages
This path is divided into 4 stages covering 24 topics. Work through each stage in order for the best learning experience.
Recommended Books for Stage 1
Pre-Algebra Mathematics
Nickels
Beginner
Elementary Algebra
Sullivan, Struve & Mazzarella
Beginner
2
Stage 2
Proof Writing Fundamentals
Learn the language of mathematical proof and logical reasoning.
Key Topics
Propositional logicPredicate logicDirect proofsContrapositionProof by contradictionMathematical induction
3 books
~6 weeks
Recommended Books for Stage 2
How to Prove It: A Structured Approach
Daniel Velleman
Beginner
Foundations of Higher Mathematics
Fletcher & Patty
Beginner
How to Read and Do Proofs
Daniel Solow
Beginner
3
Stage 3
Pre-Calculus & Trigonometry
All the algebra and trigonometry needed before tackling calculus.
Key Topics
Functions and graphsPolynomial and rational functionsExponentials and logarithmsTrigonometric functionsIdentities and equationsVectors introduction
3 books
~8 weeks
Recommended Books for Stage 3
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Precalculus: Mathematics for Calculus
Stewart, Redlin & Watson
Beginner
A Graphical Approach to Algebra and Trigonometry
Hornsby, Lial & Rockswold
Beginner
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Trigonometry Workbook
Chris McMullen
Beginner
4
Stage 4
Discrete Mathematics
The mathematics of counting, logic, and discrete structures.
Key Topics
Set theoryCombinatoricsRelations and functionsGraph theory basicsBoolean algebraRecurrence relations
2 books
~4 weeks
Recommended Books for Stage 4
Discrete Mathematical Structures
Kolman, Busby & Ross
Beginner
Discrete Mathematics and Its Applications
Rosen
Intermediate
All Books in This Path
Complete list of 10 recommended books across all stages. You don't need to buy them all — pick what works for you.
Pre-Algebra Mathematics
by Nickels
Great book for learning the very basics of algebra. Perfect starting point for absolute beginners.
Elementary Algebra
by Sullivan, Struve & Mazzarella
Modern book with tons of examples. Teaches all the algebra you need to proceed in mathematics.
How to Prove It: A Structured Approach
by Daniel Velleman
The author's favorite! Very affordable. Explains things in multiple ways. Falls back on logic which is key. Cannot recommend enough!
Foundations of Higher Mathematics
by Fletcher & Patty
Highly recommended for learning to write proofs. Great alternate explanations.
How to Read and Do Proofs
by Daniel Solow
Recommended by a former professor. Excellent for learning proof techniques.
Precalculus: Mathematics for Calculus
by Stewart, Redlin & Watson
Solid book with everything needed for calculus. By the famous James Stewart.
A Graphical Approach to Algebra and Trigonometry
by Hornsby, Lial & Rockswold
Really liked for teaching precalc and trig. Great examples, exercises, and explanations.
Trigonometry Workbook
by Chris McMullen
Unique workbook you can write in! Has answers to all problems. Focuses on topics students struggle with.
Discrete Mathematical Structures
by Kolman, Busby & Ross
Super beginner-friendly. Teaches logic which is a precursor to writing mathematical proofs.
Discrete Mathematics and Its Applications
by Rosen
Widely used in US discrete math courses. Tough read but solid content.
What's Next?
Complete this path and continue your mathematical journey.