What to include in an introduction on number theory?

Click For Summary
SUMMARY

This discussion focuses on crafting an introduction for a first course in elementary number theory, emphasizing key topics such as linear Diophantine equations, modular arithmetic (including Fermat's Little Theorem and Euler's Generalization), quadratic residues, and non-linear Diophantine equations. The author seeks to establish connections between these topics to engage potential students effectively. Notable applications of modular arithmetic, such as RSA encryption and error-correcting codes, are highlighted as motivational tools for students.

PREREQUISITES
  • Understanding of linear Diophantine equations
  • Familiarity with modular arithmetic concepts, including Fermat's Little Theorem
  • Knowledge of quadratic residues
  • Basic principles of non-linear Diophantine equations
NEXT STEPS
  • Research applications of modular arithmetic in RSA encryption
  • Explore error-correcting codes and their relation to number theory
  • Study the implications of Euler's Generalization in number theory
  • Investigate teaching strategies for linking number theory topics effectively
USEFUL FOR

Mathematics educators, students interested in number theory, and anyone looking to understand the applications of modular arithmetic in cryptography and coding theory.

matqkks
Messages
283
Reaction score
6
I am writing an introduction to a first course in elementary number theory. The topics are linear Diophantine equations, modular arithmetic including FLT and Euler's Generalization, quadratic residues and Non - linear Diophantine equations.
How can I write an introduction to this showing linkage between the various topics and hook potential students to do this course? What is the motivation on covering these topics?
 
Mathematics news on Phys.org
Here are some links I've searched yesterday on modular arithmetic and applications.

https://pdfs.semanticscholar.org/331c/f92e3155b765aede69ef8e6dedc3319f5eb6.pdf
http://www2.math.uu.se/~astrombe/talteori2016/lindahl2002.pdf
http://homepages.warwick.ac.uk/staff/J.E.Cremona/courses/MA257/ma257.pdf

Modular arithmetic alone is quite easy. During my search I came across some pages which provided a short and typical introduction:

http://www.acm.ciens.ucv.ve/main/entrenamiento/material/ModularArithmetic-Presentation.pdfhttps://euclid.ucc.ie/MATHENR/MathCircles_files/2nd and 3rd year Maths Circles/ModularArithmetic.pdf
I would take a few of those small examples and then turn to RSA as the major application here. Other interesting applications are error correcting codes or encryption in general.
 
  • Like
Likes   Reactions: member 587159

Similar threads

MHB What to include in an introduction?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Why certain topics in elementary number theory?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Why certain topics in elementary number theory?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to introduce quadratic residues?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad What should I say about elementary number theory?
  • · Replies 2 ·
Replies
2
Views
1K
MHB What should I say about elementary number theory?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Is there a resource which is good questions on quadratic
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Sum of Two Squares: Intro to Number Theory
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What resources are there for RSA for the layman?
  • · Replies 3 ·
Replies
3
Views
2K
MHB What to include on a first elementary number theory course?
  • · Replies 4 ·
Replies
4
Views
2K