Differences between revisions 29 and 37 (spanning 8 versions)
⇤ ← Revision 29 as of 2009-03-02 05:25:13 →
Size: 2736
Editor: SouravSenGupta
Comment:
← Revision 37 as of 2009-03-02 19:01:04 → ⇥
Size: 1963
Editor: ErikJacobson
Comment:
Deletions are marked like this. Additions are marked like this.
Line 1: Line 1:
= Sage for Newbies = = Sage Primers =
Line 5: Line 5:
== Major Goals : Sage Primers == == Done / In Progress ==
Line 7: Line 7:
=== Basics ===     * 0. Front Matter
Line 9: Line 9:
 * Primer Guidelines [[attachment:primer_template\example.sws]]     * 1. Basics
Line 11: Line 11:
 * Primer Design Principles [[attachment:primer_design_principles.rtf]]           * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]]
Line 13: Line 13:
 * SAGE as a Smart Calculator (target: Freshmen) [[attachment:Sage_as_a_Smart_Calculator_0.4.sws]]           * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]]
Line 15: Line 15:
=== Calculus ===           * 1.3. Sage Devel Basics [Erik, Aly]
Line 17: Line 17:
 * Differential Calculus (target: Freshmen) [[attachment:Differential_Calculus_Primer_0.3.sws]]           * 1.4. 2D and 3D Plotting in Sage [Erik]
Line 19: Line 19:
 * Integral Calculus (target: Freshmen)           * 1.5. Interact in Sage [Erik]
Line 21: Line 21:
=== Number Theory ===     * 2. Calculus
Line 23: Line 23:
 * Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]]           * 2.1. Differential Calculus [[attachment:differential_calculus.sws]]
Line 25: Line 25:
 * Number Theory via Diophantine Equations (target: Elementary Number Theory students)           * 2.2. Integral Calculus [Sourav]
Line 27: Line 27:
 * Number Theory via Primes (target: Elementary Number Theory students) [[attachment: number_theory.primes_0.1.sws]]     * 3. Linear Algebra
Line 29: Line 29:
=== Abstract Algebra ===           * 3.1. Matrix Algebra [Sourav]
Line 31: Line 31:
 * Group Theory by Robert Beezer (target: Undergraduate Math Majors) [[attachment:group_theory.sws]]     * 4. Abstract Algebra

          * 4.1. Group Theory [[attachment:group_theory.txt]] (by Robert Beezer)

    * 5. Number Theory

          * 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]]

          * 5.2. Elementary Number Theory II [Erik]

          * 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]]

          * 5.7. Quaternion Algebra [Sourav]

    * 9. About this document ...
Line 34: Line 48:
== Target
Line 36: Line 49:
1) Accessible to high school math teachers and undergraduate mathematics majors. == To Do ==
Line 38: Line 51:
2) Anticipated user desires     * 1. Basics
Line 40: Line 53:
a. Content specific modules           * 1.3. Programming in Sage
Line 42: Line 55:
i. Quadratic Forms     * 2. Calculus
Line 44: Line 57:
ii. Group theory           * 2.3. Multivariate Calculus
Line 46: Line 59:
iii. Abstract algebra           * 2.4. Taylor Series and Infinite Sums
Line 48: Line 61:
iv. Calculus           * 2.5. Differential Equations
Line 50: Line 63:
v. Number theory     * 3. Linear Algebra
Line 52: Line 65:
vi. High school algebra / trigonometry / precalculus           * 3.2. Vector Spaces [Sourav]
Line 54: Line 67:
vii. Probability     * 4. Abstract Algebra
Line 56: Line 69:
viii. Statistics           * 4.2. Rings and Fields [Erik]
Line 58: Line 71:
b. Plotting 2 and 3 dimensions     * 5. Number Theory
Line 60: Line 73:
c. Sage math functions (sage as calculator), sage constants           * 5.3. Cryptography [Dan]
Line 62: Line 75:
d. Generate Classroom examples           * 5.4. Elliptic Curves [Aly]
Line 64: Line 77:
i. show (), latex()           * 5.6. Automorphic Forms
Line 66: Line 79:
ii. matplotlab           * 5.8. Modular Forms
Line 68: Line 81:
3) Demonstrate SAGE functionality:     * 6. Combinatorics
Line 70: Line 83:
a. Primes           * 6.1. Counting
Line 72: Line 85:
b. Random numbers           * 6.2. Graph Theory
Line 74: Line 87:
c. Plotting     * 7. Geometry
Line 76: Line 89:
d. Interact     * 8. Statistics
Line 78: Line 91:
e. Sage data types           * 8.1. Statistical Methods [Erik]
Line 80: Line 93:
4) Programming           * 8.2. Probability [Erik]
Line 82: Line 95:
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
  • 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)