|
Size: 2857
Comment:
|
Size: 2036
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 1: | Line 1: |
| ------------ Major Goals: |
= Sage Primers = |
| Line 4: | Line 3: |
| 1. SAGE as a Smart Calculator (target: Freshmen) [[attachment:Sage_as_a_Smart_Calculator_0.3.sws]] [[attachment:Sage_as_a_Smart_Calculator_0.4.sws]] 2. SAGE Primers / Tutorials for (a) Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]] (b) Number Theory via Diophantine Equations (target: Elementary Number Theory students) (c) Number Theory via Primes (target: Elementary Number Theory students) (d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer] (e) Differential Calculus (target: Freshmen) [[attachment:Differential_Calculus_Primer_0.3.sws]] (f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein] (g) Primer guidelines [[attachment:primer_template\example.sws]] (3) Primer Design Principles [[attachment:primer_design_principles.rtf]] |
<<TableOfContents>> |
| Line 28: | Line 6: |
| ------------ Typesetting: |
== Done / In Progress == |
| Line 31: | Line 8: |
| * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] | |
| Line 32: | Line 10: |
| reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html] | * 1. Basics * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.4.sws]] * 1.4. Sage Devel Basics [Erik, Aly] * 2. Calculus * 2.1. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] * 2.2. Integral Calculus [Sourav] * 3. Linear Algebra * 3.1. Matrix Algebra [Sourav] * 4. Abstract Algebra * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer) * 5. Number Theory * 5.1. Elementary Number Theory I [[attachment:number_theory.primes_0.5.sws]] * 5.2. Elementary Number Theory II [Erik] * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]] * 5.7. Quaternion Algebra [Sourav] * 9. About this document ... |
| Line 36: | Line 46: |
| == To Do == | |
| Line 37: | Line 48: |
| ------------- | * 1. Basics |
| Line 39: | Line 50: |
| Goals: | * 1.3. Programming in Sage |
| Line 41: | Line 52: |
| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 1.5. 2D and 3D Plotting in Sage |
| Line 43: | Line 54: |
| 2) Anticipated user desires | * 1.6. Interact in Sage [Erik] |
| Line 45: | Line 56: |
| a. Content specific modules | * 2. Calculus |
| Line 47: | Line 58: |
| i. Quadratic Forms | * 2.3. Multivariate Calculus |
| Line 49: | Line 60: |
| ii. Group theory | * 2.4. Taylor Series and Infinite Sums |
| Line 51: | Line 62: |
| iii. Abstract algebra | * 2.5. Differential Equations |
| Line 53: | Line 64: |
| iv. Calculus | * 3. Linear Algebra |
| Line 55: | Line 66: |
| v. Number theory | * 3.2. Vector Spaces [Sourav] |
| Line 57: | Line 68: |
| vi. High school algebra / trigonometry / precalculus | * 4. Abstract Algebra |
| Line 59: | Line 70: |
| vii. Probability | * 4.2. Rings and Fields [Erik] |
| Line 61: | Line 72: |
| viii. Statistics | * 5. Number Theory |
| Line 63: | Line 74: |
| b. Plotting 2 and 3 dimensions | * 5.3. Cryptography [Dan] |
| Line 65: | Line 76: |
| c. Sage math functions (sage as calculator), sage constants | * 5.4. Elliptic Curves [Aly] |
| Line 67: | Line 78: |
| d. Generate Classroom examples | * 5.6. Automorphic Forms |
| Line 69: | Line 80: |
| i. show (), latex() | * 5.8. Modular Forms |
| Line 71: | Line 82: |
| ii. matplotlab | * 6. Combinatorics |
| Line 73: | Line 84: |
| 3) Demonstrate SAGE functionality: | * 6.1. Counting |
| Line 75: | Line 86: |
| a. Primes | * 6.2. Graph Theory |
| Line 77: | Line 88: |
| b. Random numbers | * 7. Geometry |
| Line 79: | Line 90: |
| c. Plotting | * 8. Statistics |
| Line 81: | Line 92: |
| d. Interact | * 8.1. Statistical Methods [Erik] |
| Line 83: | Line 94: |
| e. Sage data types | * 8.2. Probability [Erik] |
| Line 85: | Line 96: |
| 4) Programming a. Types, casting, relevant Sage data types b. Lists, tuples c. Control operators (if, then, else, logical operators, in, srange()) d. Loops i. For, in, srange(), range() e. Functions f. Recursion 5) Topics a. Primes and factorization i. Given a random number, is it a prime? 1. Modular division a. random() b. Factor() 2. Euclidean algorithm a. Recursion b. gcd() 3. primality testing a. for loops b. range() c. is_prime() ii. How many primes are there? 1. prime_pi() 2. plotting example iii. Where are the primes? 1. Density of primes 2. primes() 3. Arithemtic sequences of primes b. Diophantine equations i. Linear Diophantine equation 1. extended euclidean algorithm 2. recursion vs iteration ii. diagonal quadratic forms; sums of squares (ENT p. 25) 1. Pythagorean triples and generating them 2. Graphing the Pythagorean triples 3. Enumerating all triples using linear intersections 4. Elliptic curves and congruent numbers (chapter 6, stein) iii. Pell’s Equation (?) |
* 8.3. Finance |
Sage Primers
Contents
Done / In Progress
0. Sage Primer Design Principles Sage Primer Design Principles.pdf primer_design_principles.rtf
- 1. Basics
1.1. Primer Template: An Example primer_template_example.sws
1.2. Sage as a Smart Calculator basics.smart_calculator_0.4.sws
- 1.4. Sage Devel Basics [Erik, Aly]
- 2. Calculus
2.1. Differential Calculus calculus.differential_calculus_1.0.sws
- 2.2. Integral Calculus [Sourav]
- 3. Linear Algebra
- 3.1. Matrix Algebra [Sourav]
- 4. Abstract Algebra
4.1. Group Theory group_theory.sws (by Robert Beezer)
- 5. Number Theory
5.1. Elementary Number Theory I number_theory.primes_0.5.sws
- 5.2. Elementary Number Theory II [Erik]
5.5. Quadratic Forms quadratic_forms.sws
- 5.7. Quaternion Algebra [Sourav]
- 9. About this document ...
To Do
- 1. Basics
- 1.3. Programming in Sage
- 1.5. 2D and 3D Plotting in Sage
- 1.6. Interact in Sage [Erik]
- 2. Calculus
- 2.3. Multivariate Calculus
- 2.4. Taylor Series and Infinite Sums
- 2.5. Differential Equations
- 3. Linear Algebra
- 3.2. Vector Spaces [Sourav]
- 4. Abstract Algebra
- 4.2. Rings and Fields [Erik]
- 5. Number Theory
- 5.3. Cryptography [Dan]
- 5.4. Elliptic Curves [Aly]
- 5.6. Automorphic Forms
- 5.8. Modular Forms
- 6. Combinatorics
- 6.1. Counting
- 6.2. Graph Theory
- 7. Geometry
- 8. Statistics
- 8.1. Statistical Methods [Erik]
- 8.2. Probability [Erik]
- 8.3. Finance