Differences between revisions 3 and 46 (spanning 43 versions)
⇤ ← Revision 3 as of 2009-02-28 23:33:43 →
Size: 1886
Editor: ErikJacobson
Comment:
← Revision 46 as of 2009-03-11 14:06:24 → ⇥
Size: 2100
Editor: alydeines
Comment:
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:
LINKS: <<TableOfContents>>
Line 5: Line 5:
http://docutils.sourceforge.net/rst.html
Line 7: Line 6:
Sage Tutorial == Done / In Progress ==
Line 9: Line 8:
Goals:     * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]]
Line 11: Line 10:
1) Accessible to high school math teachers and undergraduate mathematics majors.     * 1. Basics
Line 13: Line 12:
2) Anticipated user desires           * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]]
Line 15: Line 14:
a. Content specific modules           * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]]
Line 17: Line 16:
i. Quadratic Forms           * 1.4. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified.
Line 19: Line 18:
ii. Group theory     * 2. Calculus
Line 21: Line 20:
iii. Abstract algebra           * 2.1. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]]
Line 23: Line 22:
iv. Calculus           * 2.2. Integral Calculus [Sourav]
Line 25: Line 24:
v. Number theory     * 3. Linear Algebra
Line 27: Line 26:
vi. High school algebra / trigonometry / precalculus           * 3.1. Matrix Algebra [Sourav]
Line 29: Line 28:
vii. Probability     * 4. Abstract Algebra
Line 31: Line 30:
viii. Statistics           * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer)
Line 33: Line 32:
b. Plotting 2 and 3 dimensions     * 5. Number Theory
Line 35: Line 34:
c. Sage math functions (sage as calculator), sage constants           * 5.1. Elementary Number Theory I [[attachment:number_theory.primes_0.5.sws]]
Line 37: Line 36:
d. Generate Classroom examples           * 5.2. Elementary Number Theory II [Erik]
Line 39: Line 38:
i. show (), latex()           * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]]
Line 41: Line 40:
ii. matplotlab           * 5.7. Quaternion Algebra [Sourav]
Line 43: Line 42:
3) Demonstrate SAGE functionality:     * 9. About this document ...
Line 45: Line 44:
a. Primes
Line 47: Line 45:
b. Random numbers
Line 49: Line 46:
c. Plotting == To Do ==
Line 51: Line 48:
d. Interact     * 1. Basics
Line 53: Line 50:
e. Sage data types           * 1.3. Programming in Sage
Line 55: Line 52:
f. Email(?)           * 1.5. 2D and 3D Plotting in Sage
Line 57: Line 54:
4) Programming           * 1.6. Interact in Sage [Erik]
Line 59: Line 56:
a. Types, casting, relevant Sage data types     * 2. Calculus
Line 61: Line 58:
b. Lists, tuples           * 2.3. Multivariate Calculus
Line 63: Line 60:
c. Control operators (if, then, else, logical operators, in, srange())           * 2.4. Taylor Series and Infinite Sums
Line 65: Line 62:
d. Loops           * 2.5. Differential Equations
Line 67: Line 64:
i. For, in, srange(), range()     * 3. Linear Algebra
Line 69: Line 66:
e. Functions           * 3.2. Vector Spaces [Sourav]
Line 71: Line 68:
f. Recursion     * 4. Abstract Algebra
Line 73: Line 70:
5) Topics           * 4.2. Rings and Fields [Erik]
Line 75: Line 72:
a. Primes and factorization     * 5. Number Theory
Line 77: Line 74:
i. Given a random number, is it a prime?           * 5.3. Cryptography [Dan]
Line 79: Line 76:
1. Modular division           * 5.4. Elliptic Curves [Aly]
Line 81: Line 78:
a. random()           * 5.6. Automorphic Forms
Line 83: Line 80:
b. Factor()           * 5.8. Modular Forms
Line 85: Line 82:
2. Euclidean algorithm     * 6. Combinatorics
Line 87: Line 84:
a. Recursion           * 6.1. Counting
Line 89: Line 86:
b. gcd()           * 6.2. Graph Theory
Line 91: Line 88:
3. primality testing     * 7. Geometry
Line 93: Line 90:
a. for loops     * 8. Statistics
Line 95: Line 92:
b. range()           * 8.1. Statistical Methods [Erik]
Line 97: Line 94:
c. is_prime()           * 8.2. Probability [Erik]
Line 99: Line 96:
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

  1. Sage Primers
    1. Done / In Progress
    2. To Do

Done / In Progress

To Do

  • 1. Basics
    • 1.3. Programming in Sage
    • 1.5. 2D and 3D Plotting in Sage
    • 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

days13/projects/sagenewbie (last edited 2011-01-28 07:12:10 by Eviatar)