## Rigorous Elementary Mathematics

Existsforall Academy presents a 4-volume series of books: Rigorous Elementary Mathematics, authored by Samer Seraj. The theme of the books is the rigorous proof of many results that are often learned by students without proof in elementary mathematics, specifically algebra, counting, number theory, and geometry. The books were written for students of mathematical contests and olympiads who want to add a rigorous foundation to their understanding of the theorems that they use, and for teachers and coaches who want to solidify their own fundamentals. To download the books, click on the cover photos. The tables of contents are provided below as a preview. To stay up to date on further projects, please sign up for the academy’s Newsletter. You might also be interested in my research Publications.

##### Volume 1: Algebra

ISBN 978-1-7389501-0-2

1. Sets and Maps
2. Arithmetic
3. Indexed Objects
4. Equality and Order
5. Special Functions
6. Closed Forms
7. Trigonometric Functions
8. Complex Numbers
10. Polynomials
11. Multivariable Inequalities
##### Volume 2: Counting

ISBN 978-1-7389501-1-9

2. Pigeonhole Principle
3. Multiplication and Division
4. Double Counting
5. Algebraic Counting
6. Principle of Inclusion-Exclusion
7. Distributions
8. Graph Theory
9. Probability
10. Classic Recursions
11. Linear Recurrences
12. Group Theory
##### Volume 3: Number Theory

ISBN 978-1-7389501-2-6

1. Divisibility
2. Primes
3. Arithmetic Functions
4. Modular Arithmetic
5. Diophantine Analysis
6. Linear Diophantine Equations
7. Base Representations I
8. Combinatorial Expressions
9. Modular Exponentiation
10. Base Representations II
11. Modular Power Residues
12. Special Forms of Integers
13. Difference and Sum of Powers
##### Volume 4: Geometry

ISBN 978-1-7389501-3-3

1. Lines
2. Angles
3. Transformations
4. Dot Product
5. Polygons
6. Circles I
7. Classifications
8. Circles II
9. Area
10. Cevians
11. Triangle Centers
12. Conics
13. Cross Product
14. Three Dimensions