|
Size: 2638
Comment:
|
Size: 2339
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) | <<TableOfContents>> |
| Line 6: | Line 5: |
| 2. SAGE Primers / Tutorials for | |
| Line 8: | Line 6: |
| (a) Quadratic Forms (target: Arizona Winter School Participants) [BR] (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) [http://sage.math.washington.edu/home/wdj/teaching/calc1-sage/ by David Joyner] (f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein] |
== Done / In Progress == * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] * 1. Basics * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman * 1.4. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]] * 2. Calculus * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] * 2.3. 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 [Erik] [[attachment:number_theory.primes_diophantine_equations.1.0.sws]] * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]] * 5.7. Quaternion Algebra [Sourav] * 9. About this document ... |
| Line 17: | Line 48: |
| ------------ Typesetting: |
== To Do == |
| Line 20: | Line 50: |
| * 1. Basics | |
| Line 21: | Line 52: |
| reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html] | * 1.3. Programming in Sage |
| Line 23: | Line 54: |
| * 1.5. 2D and 3D Plotting in Sage [JoseGuzman] | |
| Line 24: | Line 56: |
| * 1.6. Interact in Sage [Erik] | |
| Line 25: | Line 58: |
| * 2. Calculus | |
| Line 26: | Line 60: |
| ------------- | * 2.3. Multivariate Calculus |
| Line 28: | Line 62: |
| Goals: | * 2.4. Taylor Series and Infinite Sums |
| Line 30: | Line 64: |
| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 2.5. Differential Equations |
| Line 32: | Line 66: |
| 2) Anticipated user desires | * 3. Linear Algebra |
| Line 34: | Line 68: |
| a. Content specific modules | * 3.2. Vector Spaces [Sourav] |
| Line 36: | Line 70: |
| i. Quadratic Forms | * 4. Abstract Algebra |
| Line 38: | Line 72: |
| ii. Group theory | * 4.2. Rings and Fields [Erik] |
| Line 40: | Line 74: |
| iii. Abstract algebra | * 5. Number Theory |
| Line 42: | Line 76: |
| iv. Calculus | * 5.3. Cryptography [Dan] |
| Line 44: | Line 78: |
| v. Number theory | * 5.4. Elliptic Curves [Aly] |
| Line 46: | Line 80: |
| vi. High school algebra / trigonometry / precalculus | * 5.6. Automorphic Forms |
| Line 48: | Line 82: |
| vii. Probability | * 5.8. Modular Forms |
| Line 50: | Line 84: |
| viii. Statistics | * 6. Combinatorics |
| Line 52: | Line 86: |
| b. Plotting 2 and 3 dimensions | * 6.1. Counting |
| Line 54: | Line 88: |
| c. Sage math functions (sage as calculator), sage constants | * 6.2. Graph Theory |
| Line 56: | Line 90: |
| d. Generate Classroom examples | * 7. Geometry |
| Line 58: | Line 92: |
| i. show (), latex() | * 8. Statistics |
| Line 60: | Line 94: |
| ii. matplotlab | * 8.1. Statistical Methods [Erik] |
| Line 62: | Line 96: |
| 3) Demonstrate SAGE functionality: | * 8.2. Probability [Erik] |
| Line 64: | Line 98: |
| a. Primes b. Random numbers c. Plotting d. Interact e. Sage data types f. Email(?) 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_0.5.sws
1.3. Basic 2D plotting with Sage Ploting_with_Sage_v1.0.1.sws by Jose Guzman
1.4. Sage Devel Basics [Erik, Aly] dev_for_newbies.html-this needs to be restified., development_for_newbies.sws
- 2. Calculus
2.1. Limits Calculus Analysis_tutorial_Limits_v1.0.2.sws by Jose Guzman
2.2. Differential Calculus calculus.differential_calculus_1.0.sws
- 2.3. 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 [Erik] number_theory.primes_diophantine_equations.1.0.sws
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 [JoseGuzman]
- 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