We have written a trilogy of books called: Rigorous Elementary Mathematics. The theme of the books is the rigorous proof of many results that are often learned by students without proof in elementary mathematics, specifically in algebra, combinatorics, and number theory. It is currently in editing stage with a potential release date by the end of 2023! The cumulative number of pages is over 700. We are considering publication options at the moment. The tables of contents are provided below as a sample. To stay up to date on this project, please sign up for our Newsletter. You might also be interested in our research Publications.


  1. Sets and Maps
  2. Arithmetic
  3. Indexed Objects
  4. Equality and Order
  5. Special Functions
  6. Closed Forms
  7. Complex Numbers
  8. Cartesian and Complex Plane
  9. Polynomials I
  10. Polynomials II
  11. Multivariable Inequalities
  12. Vectors


  1. Addition and Subtraction
  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 I
  10. Probability II
  11. Classic Recursions
  12. Linear Recurrences

Number Theory

  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 Representation II
  11. Modular Power Residues
  12. Special Forms of Integers