Differences between revisions 7 and 60 (spanning 53 versions)
⇤ ← Revision 7 as of 2009-03-01 00:45:39 →
Size: 2671
Editor: SouravSenGupta
Comment:
← Revision 60 as of 2009-12-07 15:13:58 → ⇥
Size: 2472
Editor: Minh Nguyen
Comment: a todo note
Deletions are marked like this. Additions are marked like this.
Line 1: Line 1:
------------
Major Goals:
------------		 = Sage Primers =
Line 5: Line 3:
1. SAGE as a Smart Calculator (target: Freshmen) <<TableOfContents>>
Line 7: 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 9: Line 7:
(a) Quadratic Forms (target: Arizona Winter School Participants) == Done / In Progress ==
Line 11: 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 13: Line 11:
(c) Number Theory via Primes (target: Elementary Number Theory students)     * 1. Basics
Line 15: Line 13:
(d) Group Theory (target: UnderGrad Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer]           * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]]
Line 17: Line 15:
(e) Differential Calculus (target: Freshmen) [http://sage.math.washington.edu/home/wdj/teaching/calc1-sage/ by David Joyner]           * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]]
Line 19: 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

          * 1.4. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]]

    * 2. Calculus

          * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman

          * 2.2. Differential Calculus [[attachment: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 [[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 23: Line 49:
------------
Typesetting:
------------		 == To Do ==
Line 27: Line 51:
reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html]     * 1. Basics
Line 29: Line 53:
          * 1.3. Programming in Sage
Line 30: Line 55:
          * 1.5. 2D and 3D Plotting in Sage [JoseGuzman]
Line 31: Line 57:
          * 1.6. Interact in Sage [Erik]
Line 32: Line 59:
-------------
Sage Tutorial
-------------		     * 2. Calculus
Line 36: Line 61:
Goals:           * 2.3. Multivariate Calculus
Line 38: Line 63:
1) Accessible to high school math teachers and undergraduate mathematics majors.           * 2.4. Taylor Series and Infinite Sums
Line 40: Line 65:
2) Anticipated user desires           * 2.5. Differential Equations
Line 42: Line 67:
a. Content specific modules     * 3. Linear Algebra
Line 44: Line 69:
i. Quadratic Forms           * 3.2. Vector Spaces [Sourav]
Line 46: Line 71:
ii. Group theory     * 4. Abstract Algebra
Line 48: Line 73:
iii. Abstract algebra           * 4.2. Rings and Fields [Erik]
Line 50: Line 75:
iv. Calculus     * 5. Number Theory
Line 52: Line 77:
v. Number theory           * 5.3. Cryptography [Dan]
Line 54: Line 79:
vi. High school algebra / trigonometry / precalculus           * 5.4. Elliptic Curves [Aly]
Line 56: Line 81:
vii. Probability           * 5.6. Automorphic Forms
Line 58: Line 83:
viii. Statistics           * 5.8. Modular Forms
Line 60: Line 85:
b. Plotting 2 and 3 dimensions     * 6. Combinatorics
Line 62: Line 87:
c. Sage math functions (sage as calculator), sage constants           * 6.1. Counting
Line 64: Line 89:
d. Generate Classroom examples           * 6.2. Graph Theory
Line 66: Line 91:
i. show (), latex()     * 7. Geometry
Line 68: Line 93:
ii. matplotlab     * 8. Statistics
Line 70: Line 95:
3) Demonstrate SAGE functionality:           * 8.1. Statistical Methods [Erik]
Line 72: Line 97:
a. Primes           * 8.2. Probability [Erik]
Line 74: Line 99:
b. Random numbers

c. Plotting

d. Interact

e. Sage data types

f. Email(?)

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

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

Todo: Polish up these primers and put them in the Sage Constructions document.

Done / In Progress

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

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