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## page was renamed from days13/projects/sagenewbiew
Major Goals:		 = Sage Primers =
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1. SAGE as a Smart Calculator (from the students' point of view) <<TableOfContents>>
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2. SAGE Primers for
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(a) Quadratic Forms == Done / In Progress ==
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(b)     * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]]
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LINKS:     * 1. Basics
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http://docutils.sourceforge.net/rst.html           * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]]
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Sage Tutorial           * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]]
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Goals:           * 1.3. Basic 2D plotting with Sage [[attachment:Plotting_with_Sage.sws]] by Jose Guzman
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1) Accessible to high school math teachers and undergraduate mathematics majors.           * 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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2) Anticipated user desires     * 2. Calculus
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a. Content specific modules           * 2.1. Limits Calculus [Jose Guzman]
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i. Quadratic Forms           * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]]
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ii. Group theory           * 2.3. Integral Calculus [Sourav]
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iii. Abstract algebra     * 3. Linear Algebra
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iv. Calculus           * 3.1. Matrix Algebra [Sourav]
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v. Number theory     * 4. Abstract Algebra
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vi. High school algebra / trigonometry / precalculus           * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer)
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vii. Probability     * 5. Number Theory
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viii. Statistics           * 5.1. Elementary Number Theory I [[attachment:number_theory.primes_0.5.sws]]
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b. Plotting 2 and 3 dimensions           * 5.2. Elementary Number Theory II [Erik]
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c. Sage math functions (sage as calculator), sage constants           * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]]
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d. Generate Classroom examples           * 5.7. Quaternion Algebra [Sourav]
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i. show (), latex()     * 9. About this document ...
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ii. matplotlab
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3) Demonstrate SAGE functionality:
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a. Primes == To Do ==
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b. Random numbers     * 1. Basics
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c. Plotting           * 1.3. Programming in Sage
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d. Interact           * 1.5. 2D and 3D Plotting in Sage [JoseGuzman]
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e. Sage data types           * 1.6. Interact in Sage [Erik]
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f. Email(?)     * 2. Calculus
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4) Programming           * 2.3. Multivariate Calculus
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a. Types, casting, relevant Sage data types           * 2.4. Taylor Series and Infinite Sums
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b. Lists, tuples           * 2.5. Differential Equations
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c. Control operators (if, then, else, logical operators, in, srange())     * 3. Linear Algebra
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d. Loops           * 3.2. Vector Spaces [Sourav]
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i. For, in, srange(), range()     * 4. Abstract Algebra
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e. Functions           * 4.2. Rings and Fields [Erik]
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f. Recursion     * 5. Number Theory
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5) Topics           * 5.3. Cryptography [Dan]
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a. Primes and factorization           * 5.4. Elliptic Curves [Aly]
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i. Given a random number, is it a prime?           * 5.6. Automorphic Forms
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1. Modular division           * 5.8. Modular Forms
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a. random()     * 6. Combinatorics
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b. Factor()           * 6.1. Counting
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2. Euclidean algorithm           * 6.2. Graph Theory
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a. Recursion     * 7. Geometry
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b. gcd()     * 8. Statistics
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3. primality testing           * 8.1. Statistical Methods [Erik]
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a. for loops           * 8.2. Probability [Erik]
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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

    • 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)