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Describe days13/projects/sagenewbiew here. = Sage Primers =
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Sage Tutorial <<TableOfContents>>
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Goals:
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1) Accessible to high school math teachers and undergraduate mathematics majors. == Done / In Progress ==
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2) Anticipated user desires     * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]]
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a. Content specific modules     * 1. Basics
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i. Quadratic Forms           * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]]
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ii. Group theory           * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]]
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iii. Abstract algebra           * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1]] by Jose Guzman
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iv. Calculus           * 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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v. Number theory     * 2. Calculus
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vi. High school algebra / trigonometry / precalculus           * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman
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vii. Probability           * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]]
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viii. Statistics           * 2.3. Integral Calculus [Sourav]
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b. Plotting 2 and 3 dimensions     * 3. Linear Algebra
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c. Sage math functions (sage as calculator), sage constants           * 3.1. Matrix Algebra [Sourav]
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d. Generate Classroom examples     * 4. Abstract Algebra
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i. show (), latex()           * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer)
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ii. matplotlab     * 5. Number Theory
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3) Demonstrate SAGE functionality:           * 5.1. Elementary Number Theory [Erik] [[attachment:number_theory.primes_diophantine_equations.1.0.sws]]
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a. Primes           * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]]
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b. Random numbers           * 5.7. Quaternion Algebra [Sourav]
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c. Plotting     * 9. About this document ...
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d. Interact
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e. Sage data types
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f. Email(?) == To Do ==
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4) Programming     * 1. Basics
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a. Types, casting, relevant Sage data types           * 1.3. Programming in Sage
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b. Lists, tuples           * 1.5. 2D and 3D Plotting in Sage [JoseGuzman]
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c. Control operators (if, then, else, logical operators, in, srange())           * 1.6. Interact in Sage [Erik]
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d. Loops     * 2. Calculus
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i. For, in, srange(), range()           * 2.3. Multivariate Calculus
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e. Functions           * 2.4. Taylor Series and Infinite Sums
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f. Recursion           * 2.5. Differential Equations
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5) Topics     * 3. Linear Algebra
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a. Primes and factorization           * 3.2. Vector Spaces [Sourav]
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i. Given a random number, is it a prime?     * 4. Abstract Algebra
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1. Modular division           * 4.2. Rings and Fields [Erik]
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a. random()     * 5. Number Theory
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b. Factor()           * 5.3. Cryptography [Dan]
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2. Euclidean algorithm           * 5.4. Elliptic Curves [Aly]
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a. Recursion           * 5.6. Automorphic Forms
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b. gcd()           * 5.8. Modular Forms
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3. primality testing     * 6. Combinatorics
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a. for loops           * 6.1. Counting
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b. range()           * 6.2. Graph Theory
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c. is_prime()     * 7. Geometry
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ii. How many primes are there?     * 8. Statistics
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1. prime_pi()           * 8.1. Statistical Methods [Erik]
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2. plotting example           * 8.2. Probability [Erik]
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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)