|
Size: 2724
Comment:
|
Size: 2572
Comment: basic tutorial about solving equations with Sage
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 1: | Line 1: |
| = Sage for Newbies = | = Sage Primers = |
| Line 5: | Line 5: |
| == Major Goals : Sage Primers == | '''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document. |
| Line 7: | Line 7: |
| === Basics === | == Done / In Progress == |
| Line 9: | Line 9: |
| * Primer Guidelines [[attachment:primer_template\example.sws]] | * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] |
| Line 11: | Line 11: |
| * Primer Design Principles [[attachment:primer_design_principles.rtf]] | * 1. Basics |
| Line 13: | Line 13: |
| * SAGE as a Smart Calculator (target: Freshmen) [[attachment:sage_as_a_smart_calculator.sws]] | * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] |
| Line 15: | Line 15: |
| === Calculus === | * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] |
| Line 17: | Line 17: |
| * Differential Calculus (target: Freshmen) [[attachment:differential_calculus.sws]] | * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman |
| Line 19: | Line 19: |
| * Integral Calculus (target: Freshmen) | * 1.4. Solving basic equations with sage [[attachment:Ball_motion.sws]] by Jose Guzman |
| Line 21: | Line 21: |
| === Number Theory === | * 1.5. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]] |
| Line 23: | Line 23: |
| * Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]] | * 2. Calculus |
| Line 25: | Line 25: |
| * Number Theory via Diophantine Equations (target: Elementary Number Theory students) | * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman |
| Line 27: | Line 27: |
| * Number Theory via Primes (target: Elementary Number Theory students) [[attachment: number_theory.primes_0.1.sws]] | * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] |
| Line 29: | Line 29: |
| === Abstract Algebra === | * 2.3. Integral Calculus [Sourav] |
| Line 31: | Line 31: |
| * Group Theory by Robert Beezer (target: Undergraduate Math Majors) [[attachment:group_theory.sws]] | * 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 [Erik] [[attachment:number_theory.primes_diophantine_equations.1.0.sws]] * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]] * 5.7. Quaternion Algebra [Sourav] * 9. About this document ... |
| Line 34: | Line 50: |
| == Target == | |
| Line 36: | Line 51: |
| 1) Accessible to high school math teachers and undergraduate mathematics majors. | == To Do == |
| Line 38: | Line 53: |
| 2) Anticipated user desires | * 1. Basics |
| Line 40: | Line 55: |
| a. Content specific modules | * 1.3. Programming in Sage |
| Line 42: | Line 57: |
| i. Quadratic Forms | * 1.5. 2D and 3D Plotting in Sage [JoseGuzman] |
| Line 44: | Line 59: |
| ii. Group theory | * 1.6. Interact in Sage [Erik] |
| Line 46: | Line 61: |
| iii. Abstract algebra | * 2. Calculus |
| Line 48: | Line 63: |
| iv. Calculus | * 2.3. Multivariate Calculus |
| Line 50: | Line 65: |
| v. Number theory | * 2.4. Taylor Series and Infinite Sums |
| Line 52: | Line 67: |
| vi. High school algebra / trigonometry / precalculus | * 2.5. Differential Equations |
| Line 54: | Line 69: |
| vii. Probability | * 3. Linear Algebra |
| Line 56: | Line 71: |
| viii. Statistics | * 3.2. Vector Spaces [Sourav] |
| Line 58: | Line 73: |
| b. Plotting 2 and 3 dimensions | * 4. Abstract Algebra |
| Line 60: | Line 75: |
| c. Sage math functions (sage as calculator), sage constants | * 4.2. Rings and Fields [Erik] |
| Line 62: | Line 77: |
| d. Generate Classroom examples | * 5. Number Theory |
| Line 64: | Line 79: |
| i. show (), latex() | * 5.3. Cryptography [Dan] |
| Line 66: | Line 81: |
| ii. matplotlab | * 5.4. Elliptic Curves [Aly] |
| Line 68: | Line 83: |
| 3) Demonstrate SAGE functionality: | * 5.6. Automorphic Forms |
| Line 70: | Line 85: |
| a. Primes | * 5.8. Modular Forms |
| Line 72: | Line 87: |
| b. Random numbers | * 6. Combinatorics |
| Line 74: | Line 89: |
| c. Plotting | * 6.1. Counting |
| Line 76: | Line 91: |
| d. Interact | * 6.2. Graph Theory |
| Line 78: | Line 93: |
| e. Sage data types | * 7. Geometry |
| Line 80: | Line 95: |
| 4) Programming | * 8. Statistics |
| Line 82: | Line 97: |
| a. Types, casting, relevant Sage data types | * 8.1. Statistical Methods [Erik] |
| Line 84: | Line 99: |
| b. Lists, tuples | * 8.2. Probability [Erik] |
| Line 86: | Line 101: |
| 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
Todo: Polish up these primers and put them in the Sage Constructions document.
Done / In Progress
0. Sage Primer Design Principles Sage Primer Design Principles.pdf primer_design_principles.rtf
- 1. Basics
1.1. Primer Template: An Example primer_template_example.sws
1.2. Sage as a Smart Calculator basics.smart_calculator_0.5.sws
1.3. Basic 2D plotting with Sage Ploting_with_Sage_v1.0.1.sws by Jose Guzman
1.4. Solving basic equations with sage Ball_motion.sws by Jose Guzman
1.5. Sage Devel Basics [Erik, Aly] dev_for_newbies.html-this needs to be restified., development_for_newbies.sws
- 2. Calculus
2.1. Limits Calculus Analysis_tutorial_Limits_v1.0.2.sws by Jose Guzman
2.2. Differential Calculus calculus.differential_calculus_1.0.sws
- 2.3. Integral Calculus [Sourav]
- 3. Linear Algebra
- 3.1. Matrix Algebra [Sourav]
- 4. Abstract Algebra
4.1. Group Theory group_theory.sws (by Robert Beezer)
- 5. Number Theory
5.1. Elementary Number Theory [Erik] number_theory.primes_diophantine_equations.1.0.sws
5.5. Quadratic Forms quadratic_forms.sws
- 5.7. Quaternion Algebra [Sourav]
- 9. About this document ...
To Do
- 1. Basics
- 1.3. Programming in Sage
1.5. 2D and 3D Plotting in Sage [JoseGuzman]
- 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