1834
Comment:
|
1865
|
Deletions are marked like this. | Additions are marked like this. |
Line 1: | Line 1: |
Describe days13/projects/sagenewbiew here. | = Sage Primers = |
Line 3: | Line 3: |
Sage Tutorial | <<TableOfContents>> |
Line 5: | Line 5: |
Goals: | == Done / In Progress == |
Line 7: | Line 7: |
1) Accessible to high school math teachers and undergraduate mathematics majors. | * 0. Front Matter |
Line 9: | Line 9: |
2) Anticipated user desires | * 1. Basics |
Line 11: | Line 11: |
a. Content specific modules | * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]] |
Line 13: | Line 13: |
i. Quadratic Forms | * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]] |
Line 15: | Line 15: |
ii. Group theory | * 1.4. Sage Devel Basics [Erik, Aly] |
Line 17: | Line 17: |
iii. Abstract algebra | * 2. Calculus |
Line 19: | Line 19: |
iv. Calculus | * 2.1. Differential Calculus [[attachment:differential_calculus.sws]] |
Line 21: | Line 21: |
v. Number theory | * 2.2. Integral Calculus [Sourav] |
Line 23: | Line 23: |
vi. High school algebra / trigonometry / precalculus | * 3. Linear Algebra |
Line 25: | Line 25: |
vii. Probability | * 3.1. Matrix Algebra [Sourav] |
Line 27: | Line 27: |
viii. Statistics | * 4. Abstract Algebra |
Line 29: | Line 29: |
b. Plotting 2 and 3 dimensions | * 4.1. Group Theory [[attachment:group_theory.txt]] (by Robert Beezer) |
Line 31: | Line 31: |
c. Sage math functions (sage as calculator), sage constants | * 5. Number Theory |
Line 33: | Line 33: |
d. Generate Classroom examples | * 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]] |
Line 35: | Line 35: |
i. show (), latex() | * 5.2. Elementary Number Theory II [Erik] |
Line 37: | Line 37: |
ii. matplotlab | * 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]] |
Line 39: | Line 39: |
3) Demonstrate SAGE functionality: | * 5.7. Quaternion Algebra [Sourav] |
Line 41: | Line 41: |
a. Primes | * 9. About this document ... |
Line 43: | Line 43: |
b. Random numbers | |
Line 45: | Line 44: |
c. Plotting | |
Line 47: | Line 45: |
d. Interact | == To Do == |
Line 49: | Line 47: |
e. Sage data types | * 1. Basics |
Line 51: | Line 49: |
f. Email(?) | * 1.3. Programming in Sage |
Line 53: | Line 51: |
4) Programming | * 2. Calculus |
Line 55: | Line 53: |
a. Types, casting, relevant Sage data types | * 2.3. Multivariate Calculus |
Line 57: | Line 55: |
b. Lists, tuples | * 2.4. Taylor Series and Infinite Sums |
Line 59: | Line 57: |
c. Control operators (if, then, else, logical operators, in, srange()) | * 2.5. Differential Equations |
Line 61: | Line 59: |
d. Loops | * 3. Linear Algebra |
Line 63: | Line 61: |
i. For, in, srange(), range() | * 3.2. Vector Spaces [Sourav] |
Line 65: | Line 63: |
e. Functions | * 4. Abstract Algebra |
Line 67: | Line 65: |
f. Recursion | * 4.2. Rings and Fields [Erik] |
Line 69: | Line 67: |
5) Topics | * 5. Number Theory |
Line 71: | Line 69: |
a. Primes and factorization | * 5.3. Cryptography [Dan] |
Line 73: | Line 71: |
i. Given a random number, is it a prime? | * 5.4. Elliptic Curves [Aly] |
Line 75: | Line 73: |
1. Modular division | * 5.6. Automorphic Forms |
Line 77: | Line 75: |
a. random() | * 5.8. Modular Forms |
Line 79: | Line 77: |
b. Factor() | * 6. Combinatorics |
Line 81: | Line 79: |
2. Euclidean algorithm | * 6.1. Counting |
Line 83: | Line 81: |
a. Recursion | * 6.2. Graph Theory |
Line 85: | Line 83: |
b. gcd() | * 7. Geometry |
Line 87: | Line 85: |
3. primality testing | * 8. Statistics |
Line 89: | Line 87: |
a. for loops | * 8.1. Statistical Methods [Erik] |
Line 91: | Line 89: |
b. range() | * 8.2. Probability [Erik] |
Line 93: | Line 91: |
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
- 1.4. Sage Devel Basics [Erik, Aly]
- 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