|
Size: 2821
Comment:
|
← Revision 64 as of 2011-01-28 07:12:10 ⇥
Size: 2572
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]] |
<<TableOfContents>> |
| Line 8: | Line 5: |
| 2. SAGE Primers / Tutorials for | '''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document. |
| Line 10: | Line 7: |
| (a) Quadratic Forms (target: Arizona Winter School Participants) | == Done / In Progress == |
| Line 12: | Line 9: |
| (b) Number Theory via Diophantine Equations (target: Elementary Number Theory students) | * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] |
| Line 14: | Line 11: |
| (c) Number Theory via Primes (target: Elementary Number Theory students) | * 1. Basics |
| Line 16: | Line 13: |
| (d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer] | * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] |
| Line 18: | Line 15: |
| (e) Differential Calculus (target: Freshmen) [[attachment:Differential_Calculus_Primer_0.3.sws]] |
* 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] |
| Line 21: | Line 17: |
| (f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein] | * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman |
| Line 23: | Line 19: |
| (g) Primer guidelines [[attachment:primer_template\example.sws]] | * 1.4. Solving basic equations with Sage [[attachment:Ball_motion.sws]] by Jose Guzman |
| Line 25: | Line 21: |
| (3) Primer Design Principles [[attachment:primer_design_principles.rtf]] | * 1.5. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]] |
| Line 27: | Line 23: |
| * 2. Calculus | |
| Line 28: | Line 25: |
| ------------ Typesetting: |
* 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman |
| Line 31: | Line 27: |
| * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] | |
| Line 32: | Line 29: |
| reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html] | * 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 36: | Line 51: |
| == To Do == | |
| Line 37: | Line 53: |
| ------------- | * 1. Basics |
| Line 39: | Line 55: |
| Goals: | * 1.3. Programming in Sage |
| Line 41: | Line 57: |
| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 1.5. 2D and 3D Plotting in Sage [JoseGuzman] |
| Line 43: | Line 59: |
| 2) Anticipated user desires | * 1.6. Interact in Sage [Erik] |
| Line 45: | Line 61: |
| a. Content specific modules | * 2. Calculus |
| Line 47: | Line 63: |
| i. Quadratic Forms | * 2.3. Multivariate Calculus |
| Line 49: | Line 65: |
| ii. Group theory | * 2.4. Taylor Series and Infinite Sums |
| Line 51: | Line 67: |
| iii. Abstract algebra | * 2.5. Differential Equations |
| Line 53: | Line 69: |
| iv. Calculus | * 3. Linear Algebra |
| Line 55: | Line 71: |
| v. Number theory | * 3.2. Vector Spaces [Sourav] |
| Line 57: | Line 73: |
| vi. High school algebra / trigonometry / precalculus | * 4. Abstract Algebra |
| Line 59: | Line 75: |
| vii. Probability | * 4.2. Rings and Fields [Erik] |
| Line 61: | Line 77: |
| viii. Statistics | * 5. Number Theory |
| Line 63: | Line 79: |
| b. Plotting 2 and 3 dimensions | * 5.3. Cryptography [Dan] |
| Line 65: | Line 81: |
| c. Sage math functions (sage as calculator), sage constants | * 5.4. Elliptic Curves [Aly] |
| Line 67: | Line 83: |
| d. Generate Classroom examples | * 5.6. Automorphic Forms |
| Line 69: | Line 85: |
| i. show (), latex() | * 5.8. Modular Forms |
| Line 71: | Line 87: |
| ii. matplotlab | * 6. Combinatorics |
| Line 73: | Line 89: |
| 3) Demonstrate SAGE functionality: | * 6.1. Counting |
| Line 75: | Line 91: |
| a. Primes | * 6.2. Graph Theory |
| Line 77: | Line 93: |
| b. Random numbers | * 7. Geometry |
| Line 79: | Line 95: |
| c. Plotting | * 8. Statistics |
| Line 81: | Line 97: |
| d. Interact | * 8.1. Statistical Methods [Erik] |
| Line 83: | Line 99: |
| e. Sage data types | * 8.2. Probability [Erik] |
| Line 85: | Line 101: |
| 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
Todo: Polish up these primers and put them in the Sage Constructions document.
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. Solving basic equations with Sage Ball_motion.sws by Jose Guzman
1.5. 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