Differences between revisions 27 and 63 (spanning 36 versions)
⇤ ← Revision 27 as of 2009-03-02 05:16:44 →
Size: 2910
Editor: SouravSenGupta
Comment:
← Revision 63 as of 2011-01-06 14:54:28 → ⇥
Size: 2909
Editor: Valod Malod
Comment:
Deletions are marked like this. Additions are marked like this.
Line 1: Line 1:
= Sage for Newbies = = Sage Primers =
Line 3: Line 3:
<<TableofContents>> <<TableOfContents>>
Line 5: Line 5:
== Major Goals : Sage Primers == '''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document.
Line 7: Line 7:
=== Basics === == Done / In Progress ==
Line 9: Line 9:
 * SAGE as a Smart Calculator (target: Freshmen) [[attachment:Sage_as_a_Smart_Calculator_0.3.sws]] [[attachment:Sage_as_a_Smart_Calculator_0.4.sws]]     * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]]
Line 11: Line 11:
2. SAGE Primers     * 1. Basics
Line 13: Line 13:
(a) Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]]           * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]]
Line 15: Line 15:
(b) Number Theory via Diophantine Equations (target: Elementary Number Theory students)           * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]]
Line 17: Line 17:
(c) Number Theory via Primes (target: Elementary Number Theory students)           * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman
Line 19: Line 19:
(d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer]           * 1.4. Solving basic equations with Sage [[attachment:Ball_motion.sws]] by Jose Guzman
Line 21: Line 21:
(e) Differential Calculus (target: Freshmen)
[[attachment:Differential_Calculus_Primer_0.3.sws]]		           * 1.5. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]]
Line 24: Line 23:
(f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein]     * 2. Calculus
Line 26: Line 25:
(g) Primer guidelines [[attachment:primer_template\example.sws]]           * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman
Line 28: Line 27:
(3) Primer Design Principles [[attachment:primer_design_principles.rtf]]           * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]]
Line 30: Line 29:
          * 2.3. Integral Calculus [Sourav]
Line 31: Line 31:
------------
Typesetting:		     * 3. Linear Algebra
Line 34: Line 33:
          * 3.1. Matrix Algebra [Sourav]
Line 35: Line 35:
reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html]     * 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 39: Line 51:
== To Do ==
Line 40: Line 53:
-------------     * 1. Basics
Line 42: Line 55:
Goals:           * 1.3. Programming in Sage
Line 44: Line 57:
1) Accessible to high school math teachers and undergraduate mathematics majors.           * 1.5. 2D and 3D Plotting in Sage [JoseGuzman]
Line 46: Line 59:
2) Anticipated user desires           * 1.6. Interact in Sage [Erik]
Line 48: Line 61:
a. Content specific modules     * 2. Calculus
Line 50: Line 63:
i. Quadratic Forms           * 2.3. Multivariate Calculus
Line 52: Line 65:
ii. Group theory           * 2.4. Taylor Series and Infinite Sums
Line 54: Line 67:
iii. Abstract algebra           * 2.5. Differential Equations
Line 56: Line 69:
iv. Calculus     * 3. Linear Algebra
Line 58: Line 71:
v. Number theory           * 3.2. Vector Spaces [Sourav]
Line 60: Line 73:
vi. High school algebra / trigonometry / precalculus     * 4. Abstract Algebra
Line 62: Line 75:
vii. Probability           * 4.2. Rings and Fields [Erik]
Line 64: Line 77:
viii. Statistics     * 5. Number Theory
Line 66: Line 79:
b. Plotting 2 and 3 dimensions           * 5.3. Cryptography [Dan]
Line 68: Line 81:
c. Sage math functions (sage as calculator), sage constants           * 5.4. Elliptic Curves [Aly]
Line 70: Line 83:
d. Generate Classroom examples           * 5.6. Automorphic Forms
Line 72: Line 85:
i. show (), latex()           * 5.8. Modular Forms
Line 74: Line 87:
ii. matplotlab     * 6. Combinatorics
Line 76: Line 89:
3) Demonstrate SAGE functionality:           * 6.1. Counting
Line 78: Line 91:
a. Primes           * 6.2. Graph Theory
Line 80: Line 93:
b. Random numbers     * 7. Geometry
Line 82: Line 95:
c. Plotting     * 8. Statistics
Line 84: Line 97:
d. Interact           * 8.1. Statistical Methods [Erik]
Line 86: Line 99:
e. Sage data types           * 8.2. Probability [Erik]
Line 88: Line 101:
4) Programming           * 8.3. Finance
Line 90: Line 103:
a. Types, casting, relevant Sage data types
Line 92: Line 104:
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 (?)		  * [[http://paydayloansinmaryland.com|Payday Loans in Maryland]]
 * [[http://carrentalbirmingham.org|car rental birmingham]]
 * [[http://fxnewstrading.net|FX News Trading]]
 * [[http://fxnewstrading.net|Forex News Trading]]
 * [[http://1500cashadvance.org|1500 cash advance]]
 * [[http://1000loanpayday.org|1000 loan payday]]

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)