Number Theory: In Context and Interactive by Karl-Dieter Crisman
Number Theory: In Context and Interactive - Table of Contents
1. Prologue
2. Basic Integer Division
3. From Linear Equations to Geometry
4. First Steps with Congruence
5. Linear Congruences
6. Prime Time
7. First Steps With General Congruences
8. The Group of Integers Modulo n
9. The Group of Units and Euler’s Function
10. Primitive Roots
11. An Introduction to Cryptography
12. Some Theory Behind Cryptography
13. Sums of Squares
14. Beyond Sums of Squares
15. Points on Curves
16. Solving Quadratic Congruences
17. Quadratic Reciprocity
18. An Introduction to Functions
19. Counting and Summing Divisors
20. Long-Term Function Behavior
21. The Prime Counting Function
22. More on Prime Numbers
23. New Functions from Old
24. Infinite Sums and Products
25. Further Up and Further In
A. List of Sage Notes
B. List of Historical Remarks
C. Notation
D. List of Figures
E. References and Further Resources
What You Will Learn in Number Theory: In Context and Interactive
"Number Theory: In Context and Interactive" by "Karl-Dieter Crisman" is a comprehensive and engaging textbook designed for students beginning their study of "number theory". The book introduces foundational topics such as "modular arithmetic", "congruences", and "prime numbers", gradually building to more advanced subjects like quadratic reciprocity, arithmetic functions, and basic analytic number theory. Crisman emphasizes clear explanations, logical progression, and the interconnectedness of number theory with other areas of mathematics, making it accessible to both undergraduate students and self-learners.
A standout feature of the text is its "interactive" approach. Concepts are supported with computational examples using open-source software like "SageMath", allowing students to run code, test conjectures, and explore patterns as they learn. The book includes hundreds of exercises, blending traditional proof-based problems with computational experiments to reinforce understanding and encourage active engagement. This approach bridges theory and practice, making abstract concepts tangible and fostering deeper comprehension.
In addition, Crisman highlights practical applications of number theory, particularly in "cryptography", showing how the mathematical principles underpin modern digital security. The textbook is freely available in HTML, PDF, and print formats, making it highly accessible for classroom use or independent study. With its combination of rigorous theory, computational interaction, and real-world context, it serves as an excellent resource for learning number theory effectively.
Book Details & Specifications
Title:
Number Theory: In Context and Interactive by Karl-Dieter Crisman
Publisher:
Karl-Dieter Crisman
Year:
2024
Pages:
518
Type:
PDF
Language:
English
ISBN-10 #:
B08XLGFMNR
ISBN-13 #:
979-8713540685
License:
CC BY-ND 4.0
Amazon:
Amazon
About the Author: Karl-Dieter Crisman
The author
Karl-Dieter Crisman
is an American mathematician and professor at the "University of Northern Colorado", known for his work in "number theory" and innovative mathematics teaching. He emphasizes clarity, real-world applications, and interactive learning to engage students in understanding complex concepts. His book, "Number Theory: In Context and Interactive", introduces fundamental topics such as "primes", "divisibility", "modular arithmetic", and "congruences" through historical context and interactive examples.
Read or Downloadable Number Theory: In Context and Interactive
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