|
Size: 1995
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: |
| ## page was renamed from days13/projects/sagenewbiew Major Goals: |
= Sage Primers = |
| Line 4: | Line 3: |
| 1. SAGE as a Smart Calculator (from the students' point of view) 2. SAGE Primers |
<<TableOfContents>> |
| Line 7: | Line 5: |
| LINKS: | '''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document. |
| Line 9: | Line 7: |
| http://docutils.sourceforge.net/rst.html | == Done / In Progress == |
| Line 11: | Line 9: |
| Sage Tutorial | * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] |
| Line 13: | Line 11: |
| Goals: | * 1. Basics |
| Line 15: | Line 13: |
| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] |
| Line 17: | Line 15: |
| 2) Anticipated user desires | * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] |
| Line 19: | Line 17: |
| a. Content specific modules | * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman |
| Line 21: | Line 19: |
| i. Quadratic Forms | * 1.4. Solving basic equations with Sage [[attachment:Ball_motion.sws]] by Jose Guzman |
| Line 23: | Line 21: |
| ii. Group theory | * 1.5. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]] |
| Line 25: | Line 23: |
| iii. Abstract algebra | * 2. Calculus |
| Line 27: | Line 25: |
| iv. Calculus | * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman |
| Line 29: | Line 27: |
| v. Number theory | * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] |
| Line 31: | Line 29: |
| vi. High school algebra / trigonometry / precalculus | * 2.3. Integral Calculus [Sourav] |
| Line 33: | Line 31: |
| vii. Probability | * 3. Linear Algebra |
| Line 35: | Line 33: |
| viii. Statistics | * 3.1. Matrix Algebra [Sourav] |
| Line 37: | Line 35: |
| b. Plotting 2 and 3 dimensions | * 4. Abstract Algebra |
| Line 39: | Line 37: |
| c. Sage math functions (sage as calculator), sage constants | * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer) |
| Line 41: | Line 39: |
| d. Generate Classroom examples | * 5. Number Theory |
| Line 43: | Line 41: |
| i. show (), latex() | * 5.1. Elementary Number Theory [Erik] [[attachment:number_theory.primes_diophantine_equations.1.0.sws]] |
| Line 45: | Line 43: |
| ii. matplotlab | * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]] |
| Line 47: | Line 45: |
| 3) Demonstrate SAGE functionality: | * 5.7. Quaternion Algebra [Sourav] |
| Line 49: | Line 47: |
| a. Primes | * 9. About this document ... |
| Line 51: | Line 49: |
| b. Random numbers | |
| Line 53: | Line 50: |
| c. Plotting | |
| Line 55: | Line 51: |
| d. Interact | == To Do == |
| Line 57: | Line 53: |
| e. Sage data types | * 1. Basics |
| Line 59: | Line 55: |
| f. Email(?) | * 1.3. Programming in Sage |
| Line 61: | Line 57: |
| 4) Programming | * 1.5. 2D and 3D Plotting in Sage [JoseGuzman] |
| Line 63: | Line 59: |
| a. Types, casting, relevant Sage data types | * 1.6. Interact in Sage [Erik] |
| Line 65: | Line 61: |
| b. Lists, tuples | * 2. Calculus |
| Line 67: | Line 63: |
| c. Control operators (if, then, else, logical operators, in, srange()) | * 2.3. Multivariate Calculus |
| Line 69: | Line 65: |
| d. Loops | * 2.4. Taylor Series and Infinite Sums |
| Line 71: | Line 67: |
| i. For, in, srange(), range() | * 2.5. Differential Equations |
| Line 73: | Line 69: |
| e. Functions | * 3. Linear Algebra |
| Line 75: | Line 71: |
| f. Recursion | * 3.2. Vector Spaces [Sourav] |
| Line 77: | Line 73: |
| 5) Topics | * 4. Abstract Algebra |
| Line 79: | Line 75: |
| a. Primes and factorization | * 4.2. Rings and Fields [Erik] |
| Line 81: | Line 77: |
| i. Given a random number, is it a prime? | * 5. Number Theory |
| Line 83: | Line 79: |
| 1. Modular division | * 5.3. Cryptography [Dan] |
| Line 85: | Line 81: |
| a. random() | * 5.4. Elliptic Curves [Aly] |
| Line 87: | Line 83: |
| b. Factor() | * 5.6. Automorphic Forms |
| Line 89: | Line 85: |
| 2. Euclidean algorithm | * 5.8. Modular Forms |
| Line 91: | Line 87: |
| a. Recursion | * 6. Combinatorics |
| Line 93: | Line 89: |
| b. gcd() | * 6.1. Counting |
| Line 95: | Line 91: |
| 3. primality testing | * 6.2. Graph Theory |
| Line 97: | Line 93: |
| a. for loops | * 7. Geometry |
| Line 99: | Line 95: |
| b. range() | * 8. Statistics |
| Line 101: | Line 97: |
| c. is_prime() | * 8.1. Statistical Methods [Erik] |
| Line 103: | Line 99: |
| ii. How many primes are there? | * 8.2. Probability [Erik] |
| Line 105: | Line 101: |
| 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