|
Size: 1995
Comment:
|
Size: 1963
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: | == Done / In Progress == |
| Line 9: | Line 7: |
| http://docutils.sourceforge.net/rst.html | * 0. Front Matter |
| Line 11: | Line 9: |
| Sage Tutorial | * 1. Basics |
| Line 13: | Line 11: |
| Goals: | * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]] |
| Line 15: | Line 13: |
| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]] |
| Line 17: | Line 15: |
| 2) Anticipated user desires | * 1.3. Sage Devel Basics [Erik, Aly] |
| Line 19: | Line 17: |
| a. Content specific modules | * 1.4. 2D and 3D Plotting in Sage [Erik] |
| Line 21: | Line 19: |
| i. Quadratic Forms | * 1.5. Interact in Sage [Erik] |
| Line 23: | Line 21: |
| ii. Group theory | * 2. Calculus |
| Line 25: | Line 23: |
| iii. Abstract algebra | * 2.1. Differential Calculus [[attachment:differential_calculus.sws]] |
| Line 27: | Line 25: |
| iv. Calculus | * 2.2. Integral Calculus [Sourav] |
| Line 29: | Line 27: |
| v. Number theory | * 3. Linear Algebra |
| Line 31: | Line 29: |
| vi. High school algebra / trigonometry / precalculus | * 3.1. Matrix Algebra [Sourav] |
| Line 33: | Line 31: |
| vii. Probability | * 4. Abstract Algebra |
| Line 35: | Line 33: |
| viii. Statistics | * 4.1. Group Theory [[attachment:group_theory.txt]] (by Robert Beezer) |
| Line 37: | Line 35: |
| b. Plotting 2 and 3 dimensions | * 5. Number Theory |
| Line 39: | Line 37: |
| c. Sage math functions (sage as calculator), sage constants | * 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]] |
| Line 41: | Line 39: |
| d. Generate Classroom examples | * 5.2. Elementary Number Theory II [Erik] |
| Line 43: | Line 41: |
| i. show (), latex() | * 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]] |
| Line 45: | Line 43: |
| ii. matplotlab | * 5.7. Quaternion Algebra [Sourav] |
| Line 47: | Line 45: |
| 3) Demonstrate SAGE functionality: | * 9. About this document ... |
| Line 49: | Line 47: |
| a. Primes | |
| Line 51: | Line 48: |
| b. Random numbers | |
| Line 53: | Line 49: |
| c. Plotting | == To Do == |
| Line 55: | Line 51: |
| d. Interact | * 1. Basics |
| Line 57: | Line 53: |
| e. Sage data types | * 1.3. Programming in Sage |
| Line 59: | Line 55: |
| f. Email(?) | * 2. Calculus |
| Line 61: | Line 57: |
| 4) Programming | * 2.3. Multivariate Calculus |
| Line 63: | Line 59: |
| a. Types, casting, relevant Sage data types | * 2.4. Taylor Series and Infinite Sums |
| Line 65: | Line 61: |
| b. Lists, tuples | * 2.5. Differential Equations |
| Line 67: | Line 63: |
| c. Control operators (if, then, else, logical operators, in, srange()) | * 3. Linear Algebra |
| Line 69: | Line 65: |
| d. Loops | * 3.2. Vector Spaces [Sourav] |
| Line 71: | Line 67: |
| i. For, in, srange(), range() | * 4. Abstract Algebra |
| Line 73: | Line 69: |
| e. Functions | * 4.2. Rings and Fields [Erik] |
| Line 75: | Line 71: |
| f. Recursion | * 5. Number Theory |
| Line 77: | Line 73: |
| 5) Topics | * 5.3. Cryptography [Dan] |
| Line 79: | Line 75: |
| a. Primes and factorization | * 5.4. Elliptic Curves [Aly] |
| Line 81: | Line 77: |
| i. Given a random number, is it a prime? | * 5.6. Automorphic Forms |
| Line 83: | Line 79: |
| 1. Modular division | * 5.8. Modular Forms |
| Line 85: | Line 81: |
| a. random() | * 6. Combinatorics |
| Line 87: | Line 83: |
| b. Factor() | * 6.1. Counting |
| Line 89: | Line 85: |
| 2. Euclidean algorithm | * 6.2. Graph Theory |
| Line 91: | Line 87: |
| a. Recursion | * 7. Geometry |
| Line 93: | Line 89: |
| b. gcd() | * 8. Statistics |
| Line 95: | Line 91: |
| 3. primality testing | * 8.1. Statistical Methods [Erik] |
| Line 97: | Line 93: |
| a. for loops | * 8.2. Probability [Erik] |
| Line 99: | Line 95: |
| 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. Front Matter
- 1. Basics
1.1. Primer Template: An Example primer_template\example.sws primer_design_principles.rtf
1.2. Sage as a Smart Calculator sage_as_a_smart_calculator.sws
- 1.3. Sage Devel Basics [Erik, Aly]
- 1.4. 2D and 3D Plotting in Sage [Erik]
- 1.5. Interact in Sage [Erik]
- 2. Calculus
2.1. Differential Calculus differential_calculus.sws
- 2.2. Integral Calculus [Sourav]
- 3. Linear Algebra
- 3.1. Matrix Algebra [Sourav]
- 4. Abstract Algebra
4.1. Group Theory group_theory.txt (by Robert Beezer)
- 5. Number Theory
5.1. Elementary Number Theory I number_theory.primes_0.1.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
- 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