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