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