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= Sage for Newbies = = Sage Primers =
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== Major Goals : Sage Primers == == Done / In Progress ==
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=== Basics ===     * 0. Front Matter
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 * Primer Guidelines [[attachment:primer_template\example.sws]]     * 1. Basics
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 * Primer Design Principles [[attachment:primer_design_principles.rtf]]           * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]]
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 * SAGE as a Smart Calculator (target: Freshmen) [[attachment:Sage_as_a_Smart_Calculator_0.4.sws]]           * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]]
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=== Calculus ===           * 1.4. Sage Devel Basics [Erik, Aly]
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 * Differential Calculus (target: Freshmen) [[attachment:Differential_Calculus_Primer_0.3.sws]]     * 2. Calculus
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 * Integral Calculus (target: Freshmen)           * 2.1. Differential Calculus [[attachment:differential_calculus.sws]]
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=== Number Theory ===           * 2.2. Integral Calculus [Sourav]
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 * Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]]     * 3. Linear Algebra
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 * Number Theory via Diophantine Equations (target: Elementary Number Theory students)           * 3.1. Matrix Algebra [Sourav]
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 * Number Theory via Primes (target: Elementary Number Theory students) [[attachment: number_theory.primes_0.1.sws]]     * 4. Abstract Algebra
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=== Abstract Algebra ===           * 4.1. Group Theory [[attachment:group_theory.txt]] (by Robert Beezer)
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 * Group Theory by Robert Beezer (target: Undergraduate Math Majors) [[attachment:group_theory.sws]]     * 5. Number Theory

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