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Major Goals: = Sage Primers =
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1. SAGE as a Smart Calculator (from the students' point of view)
2. SAGE Primers		 <<TableOfContents>>
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LINKS:
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http://docutils.sourceforge.net/rst.html == Done / In Progress ==
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Sage Tutorial     * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]]
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Goals:     * 1. Basics
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1) Accessible to high school math teachers and undergraduate mathematics majors.           * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]]
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2) Anticipated user desires           * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]]
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a. Content specific modules           * 1.3. Basic 2D plotting with Sage [[attachment:Plotting_with_Sage.sws]] by Jose Guzman
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i. Quadratic Forms           * 1.4. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]]
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ii. Group theory     * 2. Calculus
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iii. Abstract algebra           * 2.1. Limits Calculus [Jose Guzman]
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iv. Calculus           * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]]
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v. Number theory           * 2.3. Integral Calculus [Sourav]
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vi. High school algebra / trigonometry / precalculus     * 3. Linear Algebra
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vii. Probability           * 3.1. Matrix Algebra [Sourav]
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viii. Statistics     * 4. Abstract Algebra
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b. Plotting 2 and 3 dimensions           * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer)
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c. Sage math functions (sage as calculator), sage constants     * 5. Number Theory
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d. Generate Classroom examples           * 5.1. Elementary Number Theory I [[attachment:number_theory.primes_0.5.sws]]
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i. show (), latex()           * 5.2. Elementary Number Theory II [Erik]
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ii. matplotlab           * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]]
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3) Demonstrate SAGE functionality:           * 5.7. Quaternion Algebra [Sourav]
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a. Primes     * 9. About this document ...
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b. Random numbers
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c. Plotting
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d. Interact == To Do ==
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e. Sage data types     * 1. Basics
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f. Email(?)           * 1.3. Programming in Sage
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4) Programming           * 1.5. 2D and 3D Plotting in Sage [JoseGuzman]
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a. Types, casting, relevant Sage data types           * 1.6. Interact in Sage [Erik]
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b. Lists, tuples     * 2. Calculus
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c. Control operators (if, then, else, logical operators, in, srange())           * 2.3. Multivariate Calculus
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d. Loops           * 2.4. Taylor Series and Infinite Sums
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i. For, in, srange(), range()           * 2.5. Differential Equations
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e. Functions     * 3. Linear Algebra
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f. Recursion           * 3.2. Vector Spaces [Sourav]
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5) Topics     * 4. Abstract Algebra
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a. Primes and factorization           * 4.2. Rings and Fields [Erik]
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i. Given a random number, is it a prime?     * 5. Number Theory
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1. Modular division           * 5.3. Cryptography [Dan]
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a. random()           * 5.4. Elliptic Curves [Aly]
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b. Factor()           * 5.6. Automorphic Forms
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2. Euclidean algorithm           * 5.8. Modular Forms
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a. Recursion     * 6. Combinatorics
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b. gcd()           * 6.1. Counting
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3. primality testing           * 6.2. Graph Theory
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a. for loops     * 7. Geometry
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b. range()     * 8. Statistics
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c. is_prime()           * 8.1. Statistical Methods [Erik]
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ii. How many primes are there?           * 8.2. Probability [Erik]
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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)