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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 '''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document.
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    (a) Quadratic Forms (target: Arizona Winter School Participants)[[BR]]
    (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]		 == 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. Solving basic equations with Sage [[attachment:Ball_motion.sws]] by Jose Guzman

          * 1.5. 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 ...
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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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          * 1.5. 2D and 3D Plotting in Sage [JoseGuzman]
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          * 1.6. Interact in Sage [Erik]
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    * 2. Calculus
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-------------           * 2.3. Multivariate Calculus
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Goals:           * 2.4. Taylor Series and Infinite Sums
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1) Accessible to high school math teachers and undergraduate mathematics majors.           * 2.5. Differential Equations
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2) Anticipated user desires     * 3. Linear Algebra
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a. Content specific modules           * 3.2. Vector Spaces [Sourav]
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i. Quadratic Forms     * 4. Abstract Algebra
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ii. Group theory           * 4.2. Rings and Fields [Erik]
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iii. Abstract algebra     * 5. Number Theory
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iv. Calculus           * 5.3. Cryptography [Dan]
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v. Number theory           * 5.4. Elliptic Curves [Aly]
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vi. High school algebra / trigonometry / precalculus           * 5.6. Automorphic Forms
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vii. Probability           * 5.8. Modular Forms
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viii. Statistics     * 6. Combinatorics
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b. Plotting 2 and 3 dimensions           * 6.1. Counting
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c. Sage math functions (sage as calculator), sage constants           * 6.2. Graph Theory
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d. Generate Classroom examples     * 7. Geometry
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i. show (), latex()     * 8. Statistics
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ii. matplotlab           * 8.1. Statistical Methods [Erik]
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3) Demonstrate SAGE functionality:           * 8.2. Probability [Erik]
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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

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)