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| Describe days13/projects/sagenewbiew here. LINKS: http://docutils.sourceforge.net/rst.html |
= Sage for Newbies = |
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| Sage Tutorial | <<TableOfContents>> |
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| Goals: | == Done == |
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| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 0. Front Matter |
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| 2) Anticipated user desires | * 1. Basics |
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| a. Content specific modules | o 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]] |
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| i. Quadratic Forms | o 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]] |
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| ii. Group theory | * 2. Calculus |
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| iii. Abstract algebra | o 2.1. Differential Calculus [[attachment:differential_calculus.sws]] |
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| iv. Calculus | * 4. Abstract Algebra |
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| v. Number theory | o 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer) |
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| vi. High school algebra / trigonometry / precalculus | * 5. Number Theory |
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| vii. Probability | o 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]] |
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| viii. Statistics | o 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]] |
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| b. Plotting 2 and 3 dimensions | * 9. About this document ... |
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| c. Sage math functions (sage as calculator), sage constants | |
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| d. Generate Classroom examples | |
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| i. show (), latex() | == To Do == |
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| ii. matplotlab | * 1. Basics |
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| 3) Demonstrate SAGE functionality: | o 1.3. Programming in Sage |
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| a. Primes | o 1.4. Sage Devel Basics |
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| b. Random numbers | * 2. Calculus |
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| c. Plotting | o 2.2. Integral Calculus |
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| d. Interact | o 2.3. Multivariate Calculus |
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| e. Sage data types | o 2.4. Taylor Series and Infinite Sums |
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| f. Email(?) | o 2.5. Differential Equations |
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| 4) Programming | * 3. Linear Algebra |
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| a. Types, casting, relevant Sage data types | o 3.1. Matrix Algebra |
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| b. Lists, tuples | o 3.2. Vector Spaces |
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| c. Control operators (if, then, else, logical operators, in, srange()) | * 4. Abstract Algebra |
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| d. Loops | o 4.2. Rings and Fields |
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| i. For, in, srange(), range() | * 5. Number Theory |
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| e. Functions | o 5.2. Elementary Number Theory II |
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| f. Recursion | o 5.3. Cryptography |
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| 5) Topics | o 5.4. Elliptic Curves |
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| a. Primes and factorization | o 5.6. Automorphic Forms |
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| i. Given a random number, is it a prime? | o 5.7. Quaternion Algebra |
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| 1. Modular division | o 5.8. Modular Forms |
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| a. random() | * 6. Combinatorics |
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| b. Factor() | o 6.1. Counting |
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| 2. Euclidean algorithm | o 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 | o 8.1. Statistical Methods |
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| a. for loops | o 8.2. Probability |
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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 (?) |
o 8.3. Finance |
Sage for Newbies
Contents
Done
- 0. Front Matter
- 1. Basics
o 1.1. Primer Template: An Example primer_template\example.sws primer_design_principles.rtf
o 1.2. Sage as a Smart Calculator sage_as_a_smart_calculator.sws
- 2. Calculus
o 2.1. Differential Calculus differential_calculus.sws
- 4. Abstract Algebra
o 4.1. Group Theory group_theory.sws (by Robert Beezer)
- 5. Number Theory
o 5.1. Elementary Number Theory I number_theory.primes_0.1.sws
o 5.5. Quadratic Forms quadratic_forms.sws
- 9. About this document ...
To Do
- 1. Basics
- o 1.3. Programming in Sage o 1.4. Sage Devel Basics
- 2. Calculus
- o 2.2. Integral Calculus o 2.3. Multivariate Calculus o 2.4. Taylor Series and Infinite Sums o 2.5. Differential Equations
- 3. Linear Algebra
- o 3.1. Matrix Algebra o 3.2. Vector Spaces
- 4. Abstract Algebra
- o 4.2. Rings and Fields
- 5. Number Theory
- o 5.2. Elementary Number Theory II o 5.3. Cryptography o 5.4. Elliptic Curves o 5.6. Automorphic Forms o 5.7. Quaternion Algebra o 5.8. Modular Forms
- 6. Combinatorics
- o 6.1. Counting o 6.2. Graph Theory
- 7. Geometry
- 8. Statistics
- o 8.1. Statistical Methods o 8.2. Probability o 8.3. Finance