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Major Goals:		 = Sage Primers =
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1. SAGE as a Smart Calculator (target: Freshmen) <<TableOfContents>>
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2. SAGE Primers / Tutorials for == Done / In Progress ==
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    (a) Quadratic Forms (target: Arizona Winter School Participants)     * 0. Front Matter
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    * 1. Basics
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    (b) Number Theory via Diophantine Equations (target: Elementary Number Theory students)           * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]]
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          * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]]
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    (c) Number Theory via Primes (target: Elementary Number Theory students)           * 1.4. Sage Devel Basics [Erik, Aly]
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    * 2. Calculus
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    (d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer]           * 2.1. Differential Calculus [[attachment:differential_calculus.sws]]
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          * 2.2. Integral Calculus [Sourav]
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    (e) Differential Calculus (target: Freshmen) [http://sage.math.washington.edu/home/wdj/teaching/calc1-sage/ by David Joyner]     * 3. Linear Algebra
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          * 3.1. Matrix Algebra [Sourav]
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    (f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein]     * 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 ...
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Typesetting:		 == To Do ==
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    * 1. Basics
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reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html]           * 1.3. Programming in Sage
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    * 2. Calculus
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          * 2.3. Multivariate Calculus
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          * 2.4. Taylor Series and Infinite Sums
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-------------           * 2.5. Differential Equations
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Goals:     * 3. Linear Algebra
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1) Accessible to high school math teachers and undergraduate mathematics majors.           * 3.2. Vector Spaces [Sourav]
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2) Anticipated user desires     * 4. Abstract Algebra
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a. Content specific modules           * 4.2. Rings and Fields [Erik]
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i. Quadratic Forms     * 5. Number Theory
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ii. Group theory           * 5.3. Cryptography [Dan]
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iii. Abstract algebra           * 5.4. Elliptic Curves [Aly]
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iv. Calculus           * 5.6. Automorphic Forms
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v. Number theory           * 5.8. Modular Forms
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vi. High school algebra / trigonometry / precalculus     * 6. Combinatorics
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vii. Probability           * 6.1. Counting
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viii. Statistics           * 6.2. Graph Theory
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b. Plotting 2 and 3 dimensions     * 7. Geometry
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c. Sage math functions (sage as calculator), sage constants     * 8. Statistics
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d. Generate Classroom examples           * 8.1. Statistical Methods [Erik]
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i. show (), latex()           * 8.2. Probability [Erik]
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ii. matplotlab

3) Demonstrate SAGE functionality:

a. Primes

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

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)