CONTENT OUTLINE
Proving Combinatorial Identities
| Lect | Date | Topic | Distribution |
| Jan 11 | Course Overview | [PDF] |
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| Jan 13 | Wolfram Language | [NB] [PDF] | |
| Jan 18 | Martin Luther King Day |
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| 1 | Jan 20 | Solving Recurrence Equations HW 1 OUT |
[NB] [PDF] |
| 2 | Jan 25 | Sister Celine’s Algorithm | [NB] [PDF] |
| 3 | Jan 27 | Gosper’s Algorithm HW 2 OUT |
[NB] [PDF] |
| 4 | Feb 01 | Gosper’s Algorithm | |
| 5 | Feb 03 | Wilf-Zeilberger’s Algorithm | [NB] [PDF] |
| 6 | Feb 08 | Zeilberger’s Algorithm HW 3 OUT |
[NB] [PDF] |
| 7 | Feb 10 | Petkovsek’s Algorithm | [NB] [PDF] |
| 8 | Feb 15 | Proving Combinatorial Identities Harmonic Number Identities |
[NB] [PDF] |
| Feb 17 | Exam – I |
Gröbner Bases
| Lect | Date | Topic | Distribution |
| 9 | Feb 22 | Polynomial Ideals Monomial Order HW 4 OUT |
[NB] [PDF] |
| 10 | Feb 24 | Monomial Ideals Gröbner Bases |
[NB] [PDF] |
| 11 | Feb 29 | Buchberger’s Algorithm Reduced Gröbner Bases |
[NB] [PDF] |
| 12 | Mar. 02 | More on Buchberger’s Algorithm | [NB] [PDF] |
| Mar 07 | SPRING BREAK |
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| Mar 09 | SPRING BREAK |
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| Mar. 14 | Applications of Gröbner bases in geometry HW 5 OUT |
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| 13 | Mar 16 | Lagrange Multipliers | [NB] [PDF] |
| 14 | Mar 21 | Graph Coloring with Gröbner bases Solving Sudoku with Gröbner bases |
[NB] [PDF] [NB] [PDF] |
| 15 | Mar 23 | Integer Relation Algorithms | [NB] [PDF] |
| 16 | Mar 28 | Online Mathematical Tools | [NB] [PDF] |
| Mar 30 | Exam – II |
Symbolic Integration
| Lect | Date | Topic | Distribution |
| 17 | Apr. 04 | Differential Algebra Squarefree Factorization |
[NB] [PDF] |
| 18 | Apr. 06 | Squarefree Factorization Hermite-Ostrogradsky’s Algorithm Milestone-1 |
[NB] [PDF] |
| 19 | Apr. 11 | Rothstein-Trager’s Algorithm Resultants |
[NB] [PDF] |
| 20 | Apr 13 | Computing Resultants Sylvester Matrix |
[NB] [PDF] |
| 21 | Apr 18 | Rioboo’s Algorithm Milestone-2 |
[NB] [PDF] |
| 22 | Apr 20 | Logarithmic Extension | [NB] [PDF] |
| 23 | Apr 25 | Logarithmic Extension | [NB] [PDF] |
| 24 | Apr 27 | Exponential Extension | [NB] [PDF] |
| May. 05 | Project Due |