Differences between revisions 16 and 59 (spanning 43 versions)
⇤ ← Revision 16 as of 2009-03-01 14:59:58 →
Size: 2654
Editor: ErikJacobson
Comment:
← Revision 59 as of 2009-07-01 05:23:09 → ⇥
Size: 2339
Editor: was
Comment:
Deletions are marked like this. Additions are marked like this.
Line 1: Line 1:
------------
Major Goals:		 = Sage Primers =
Line 4: Line 3:
1. SAGE as a Smart Calculator (target: Freshmen)

2. SAGE Primers / Tutorials for

(a) Quadratic Forms (target: Arizona Winter School Participants)

(b) Number Theory via Diophantine Equations (target: Elementary Number Theory students)

(c) Number Theory via Primes (target: Elementary Number Theory students)

(d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer]

(e) Differential Calculus (target: Freshmen) [http://sage.math.washington.edu/home/wdj/teaching/calc1-sage/ by David Joyner]

(f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein]

(3) Port "Sage for Newbies" to ReST

------------
Typesetting:		 <<TableOfContents>>
Line 26: Line 6:
reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html] == Done / In Progress ==

    * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]]

    * 1. Basics

          * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]]

          * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]]

          * 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 30: Line 48:
== To Do ==
Line 31: Line 50:
-------------     * 1. Basics
Line 33: Line 52:
Goals:           * 1.3. Programming in Sage
Line 35: Line 54:
1) Accessible to high school math teachers and undergraduate mathematics majors.           * 1.5. 2D and 3D Plotting in Sage [JoseGuzman]
Line 37: Line 56:
2) Anticipated user desires           * 1.6. Interact in Sage [Erik]
Line 39: Line 58:
a. Content specific modules     * 2. Calculus
Line 41: Line 60:
i. Quadratic Forms           * 2.3. Multivariate Calculus
Line 43: Line 62:
ii. Group theory           * 2.4. Taylor Series and Infinite Sums
Line 45: Line 64:
iii. Abstract algebra           * 2.5. Differential Equations
Line 47: Line 66:
iv. Calculus     * 3. Linear Algebra
Line 49: Line 68:
v. Number theory           * 3.2. Vector Spaces [Sourav]
Line 51: Line 70:
vi. High school algebra / trigonometry / precalculus     * 4. Abstract Algebra
Line 53: Line 72:
vii. Probability           * 4.2. Rings and Fields [Erik]
Line 55: Line 74:
viii. Statistics     * 5. Number Theory
Line 57: Line 76:
b. Plotting 2 and 3 dimensions           * 5.3. Cryptography [Dan]
Line 59: Line 78:
c. Sage math functions (sage as calculator), sage constants           * 5.4. Elliptic Curves [Aly]
Line 61: Line 80:
d. Generate Classroom examples           * 5.6. Automorphic Forms
Line 63: Line 82:
i. show (), latex()           * 5.8. Modular Forms
Line 65: Line 84:
ii. matplotlab     * 6. Combinatorics
Line 67: Line 86:
3) Demonstrate SAGE functionality:           * 6.1. Counting
Line 69: Line 88:
a. Primes           * 6.2. Graph Theory
Line 71: Line 90:
b. Random numbers     * 7. Geometry
Line 73: Line 92:
c. Plotting     * 8. Statistics
Line 75: Line 94:
d. Interact           * 8.1. Statistical Methods [Erik]
Line 77: Line 96:
e. Sage data types           * 8.2. Probability [Erik]
Line 79: Line 98:
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

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)