### General Math Study Advice

### Course Notes

**Magic Box Cheat Sheet****RSA Cheat Sheet****Midterm Topics****Final Topics****Legendre Jacobi Cheat Sheet****Coding Theory Worksheet Blank****Coding Theory Solutions**

### Books and Stories

**Official Text:***Introduction to Cryptography with Coding Theory*, 2nd Edition, Wade Trappe, Lawrence C. Washington.- Textbook Website (errata, code)

**The Code Book:**A popular history of cryptography, by Simon Singh.**David Kohel's Cryptography:**A free online text with Sage. Appendices A and B are particularly useful (intro to Sage for crypto).**Elementary Number Theory: Primes, Congruences, and Secrets**An excellent place to look up Sage commands in situ with number theory and cryptography topics.**Cryptography Stories:**Some of the classics.- The Return of Sherlock Holmes by Sir Arthur Conan Doyle, includes
*The adventure of the dancing men*. - The Gold Bug by Edgar Allan Poe.

- The Return of Sherlock Holmes by Sir Arthur Conan Doyle, includes
**Further Reading:**There are always more books.- History:
*The Codebreakers*D. Kahn. - Mathematical cryptography:
*Cryptography, Theory and Practice*D. Stinson;*An Introduction to Mathematical Cryptography*, J. Hoffstein, J. Pipher and J. Silverman;*A Course in Number Theory and Cryptography*, N. Koblitz;*Algebraic Aspects of Cryptography*, N. Koblitz. - Coding:
*A First Course in Coding Theory*R. Hill;*Elements of Algebraic Coding Theory*, L. Vermani;*Introduction to Coding THeory*, J. H. van Lint - Number Theory:
*A Friendly Introduction to Number Theory*J. Silverman;*The Theory of Numbers*, G. H. Hardy and E. M. Wright. - Algebra:
*A First Course in Abstract Algebra*, J. Fraleigh;*Abstract Algebra*D. S. Dummit and R. M. Foote;*Topics in Algebra*, I. Herstein;*Basic Algebra, I., II.*, N. Jacobson.

- History:
**Reading about Bitcoin**: A particularly nice account of Bitcoin can be found by Michael Nielson.

### Cryptography Resources

**Sage**- Free, sophisticated math software for indepth exploration.- CU Sage Server - please sign up for an account asap.
- Sage's documentation for Cryptography functions.
- Kohel's Cryptography - appendices have intro to cryptosystems with Sage
- Ask Sage - question and answer service from the hive mind
- Sage's Quick Reference Sheets to keep by your side.

**Campus Computer Labs**- Use Sage (via link above), Latex, Maple, Mathematica, Matlab etc.- Search by software - e.g. tex, mathematica

**Latex**- the only reasonable way to type math.- Introduction to Latex - installing and how to type.
- Detexify - To find a symbol you want to know.
- WriteLatex.Com - No need to install software or visit the lab - typeset online!
- Templates: tex file and expected output.
- Tex Stackexchange - question and answer service from the hive mind

**Wolfram Alpha**- Simple math computation without learning a syntax.**Online Cryptography Tools**- The Black Chamber - Simon Singh's online guide to historical codes and ciphers. Includes coding/decoding and cracking applets.
- Cryptool Online - Online tools and applets for many many classical and modern cryptographic systems.
- Enigma Machine Simulators and Software - The definitive online catalogue of Enigma software and everything else (including purchasing parts).
- Cipher Wheel: Java Applet and Paper Cutout - In case you've lost yours.
- US Army Naval cipher device M-94 applet - Play with it online

**State of the Art**- Current Key Sizes for Cryptography - How many bits do you need?
- Current Factorisation Records - How big can we factor?

### General Math Resources

- Dr. Math - Question answer service (by 'Math Doctors'). Use the search box first; there's a 99% chance someone has asked your question before.
- Mathematics at StackExchange - Question answer service (by the 'hive mind'). Use the search box first; there's a 98% chance someone has asked your question before.
- Math Forum Digital Library - Catalogue of web resources.

### CU Resources

- The Undergraduate Mathematics Resource Center is in Math 175 (first floor of math building), and is open M-Th 9-5 and F 9-2. Although tutors no longer serve this course, an area has been set up where you can meet your peers to work together.
- A tutor list is available.