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= Sage for Newbies = = Sage Primers =
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<<TableofContents>>

== Major Goals : Sage Primers ==

=== Basics ===

 * SAGE as a Smart Calculator (target: Freshmen) [[attachment:Sage_as_a_Smart_Calculator_0.3.sws]] [[attachment:Sage_as_a_Smart_Calculator_0.4.sws]]

2. SAGE Primers

(a) Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]]

(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)
[[attachment:Differential_Calculus_Primer_0.3.sws]]

(f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein]

(g) Primer guidelines [[attachment:primer_template\example.sws]]

(3) Primer Design Principles [[attachment:primer_design_principles.rtf]]		 <<TableOfContents>>
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Typesetting:		 == Done / In Progress ==
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    * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]]
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reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html]     * 1. Basics

          * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]]

          * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.4.sws]]

          * 1.4. Sage Devel Basics [Erik, Aly]

    * 2. Calculus

          * 2.1. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]]

          * 2.2. 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 I [[attachment:number_theory.primes_0.5.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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== To Do ==
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-------------     * 1. Basics
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Goals:           * 1.3. Programming in Sage
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1) Accessible to high school math teachers and undergraduate mathematics majors.           * 1.5. 2D and 3D Plotting in Sage
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2) Anticipated user desires           * 1.6. Interact in Sage [Erik]
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a. Content specific modules     * 2. Calculus
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i. Quadratic Forms           * 2.3. Multivariate Calculus
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ii. Group theory           * 2.4. Taylor Series and Infinite Sums
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iii. Abstract algebra           * 2.5. Differential Equations
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iv. Calculus     * 3. Linear Algebra
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v. Number theory           * 3.2. Vector Spaces [Sourav]
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vi. High school algebra / trigonometry / precalculus     * 4. Abstract Algebra
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vii. Probability           * 4.2. Rings and Fields [Erik]
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viii. Statistics     * 5. Number Theory
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b. Plotting 2 and 3 dimensions           * 5.3. Cryptography [Dan]
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c. Sage math functions (sage as calculator), sage constants           * 5.4. Elliptic Curves [Aly]
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d. Generate Classroom examples           * 5.6. Automorphic Forms
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i. show (), latex()           * 5.8. Modular Forms
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ii. matplotlab     * 6. Combinatorics
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3) Demonstrate SAGE functionality:           * 6.1. Counting
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a. Primes           * 6.2. Graph Theory
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b. Random numbers     * 7. Geometry
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c. Plotting     * 8. Statistics
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d. Interact           * 8.1. Statistical Methods [Erik]
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e. Sage data types           * 8.2. Probability [Erik]
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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
    • 1.5. 2D and 3D Plotting in Sage
    • 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)