Last updated April 2, 2012

I am an Associate Professor in the Department of Mathematics and Computer Science at Saint Mary's University in Halifax, Nova Scotia, Canada. My primary research interest is algebraic combinatorics, particularly enumerative problems underlying questions in geometry and representation theory.

** **

I can be reached by foot, e-mail, and telephone as follows:

Office: MN 123

E-mail: name.surname at smu.ca

Phone: (902) 420-5792

Mailing address:

John Irving

Dept. of Mathematics & Computing Science

Saint Mary's University

Halifax, NS, Canada

B3H 3C3

Office hours for the
**Winter 2012 Exam Period** are as follows:

- Wednesday April 4 @ 9:00-11:00am
- Thursday April 5 @ 9:00-11:00am
- Tuesday @ 9:00-11:00am
- Wednesday @ 9:00-11:00am and 1:00-3:00pm

Send me an e-mail if you wish to set up an appointment to see me outside of
office hours, or drop
by the office and see if I'm available.

**Final examination:**
The final exam will be held on *Thursday, April 12* from 9:00am-12:00pm in the Field House.

**Review session:**
I will hold a review session on *Tuesday, April 10* in Sobey 260, starting at 12:30pm.

**Office hours:**
Please see above for my office hours during the exam period.

**Course syllabus:**
Click here to download the course syllabus.

**Homework:**

Week of | Topics | Suggested Reading | Suggested Homework | Recitations |
---|---|---|---|---|

January 9 | Distance and velocity. The derivative. |
2.1, 2.7 |
2.1 #1, 5 2.7 #1, 3(a,b), 5, 7, 9(a,b), 11-19 Supplementary problems |
Pretest |

January 16 | Computing derivatives. | Read me first 3.1, 3.2, 3.4 |
3.1 #3-11, 13-15, 17-27, 33, 51 3.2 #1, 7-11, 13-15, 19, 31, 35(a), 43, 49 3.4 #3, 7-11, 17-21, 25-27, 42, 51 |
Recitation 2 and Solutions |

January 23 | More derivatives. | 1.5, App. D, 3.2, 3.3, 3.4 |
3.2 #3-6, 17-20, 34, 45 3.3 #1-19, 21, 23, 25(a) 3.4 #1-46, 51-54, 55(a), 59, 69, 71, 75 Supplementary problems |
Recitation 3 and Solutions |

January 30 | Logarithms and inverse functions. |
1.5, 1.6, 3.6 |
1.6 #1-11, 15, 19, 21-39, 45-54, 59-64 3.6 #1-15, 19-33, 37-47 Supplementary problems |
Test 1 (white) &
Solutions
Test 1 (green) & Solutions Test 1 (pink) & Solutions |

February 6 | Inverse trig functions. Implicit differentiation. Related rates. |
3.5, 3.9 |
3.5 #1-29, 33, 35, 39, 45-53, 57, 65 3.9 #3-23, 27-30, 35 (these take practice!) |
Recitation 4 and Solutions |

February 13 | Related Rates. Limits Revisited. Midterm. |
2.2, 2.3 |
Read Sections 2.2 and 2.3 2.2 #1-9, 13, 15, 25-32 2.3 #1-9, 11-29, 39-47 |
Midterm Solutions |

February 27 | Continuity. Maxima/Minima. |
2.5, 4.1 |
2.5 #1-5, 15-19, 21-27, 29, 35, 37, 41 4.1 #1-13, 15-43, 47-61 (the more the merrier) |
Recitation 5 and Solutions |

March 5 | Mean Value Theorem. Basic curve sketching. |
4.2, 4.3 |
4.2 #1-5, 11-15, 17, 21 4.3 1, 3, 4, 7, 9-21, 25, 33-43 |
Recitation 6 and Solutions |

March 12 | Limits at infinity. L'Hospital's Rule. More Curve Sketching. |
1.6, 4.3, 4.4, 4.5 |
1.6 #3, 15-25, 28-33, 39-43, 49, 51 4.3 #45-51 4.4 #5-21, 25-33, 37-51 4.5 #1-51 (do as many as needed!) |
Test 2 & Solutions |

March 19 | Optimization Problems. Area Under Curves. The Definite Integral. |
4.7, 5.1, 5.2 |
4.7 #3-35 (try a variety) 5.1 #17-21 5.2 #1, 5, 17, 19, 29, 33-39 |
Recitation 7 and Solutions |

March 26 April 2 |
Fundamental Theorem. Antiderivatives. Indefinite Integrals |
4.9, 5.3, 5.4 |
5.3 #7-41, 43, 51, 53-57 5.4 #1-3, 5-17, 21-39, 49-51, 57, 59, 61 4.9 #1-46 (as many as you need!) |
Recitation 8 and Solutions |

**Review material:** Proper preparation is essential for success in this course. The following pointers
may help you review some background material. There is no way to learn but through practice, so be sure
to work through as many problems as possible. (Notice that solutions are provided in the downloadable files.)

- For basic
*algebra*, see these notes. - For basic
*geometry*, see these notes. - For
*trigonometry*, see Appendix D of your text.

My main research interest is enumerative combinatorics (ie. counting), particularly as it relates to problems in algebra and geometry. To date I have mostly focused on problems involving factorizations in the symmetric group; that is, counting the number of ways a given permutation can be decomposed as an ordered product of other permutations with various conditions imposed on these factors (such as cycle type, minimality, transitivity). Questions of this type are intimately linked with the representation theory of the symmetric group (equivalently, the study of its group algebra), and also the geometry of branched coverings.

Preprints of my papers may be download below. My graduate work was completed under the supervision of David Jackson at the University of Waterloo (Ontario, Canada). Both my Master's and Ph.D. theses are available upon request.

*An Enumerative Problem Concerning Products of Permutations*, Master's Thesis, University of Waterloo, 1998*Combinatorial Constructions for Transitive Factorizations in the Symmetric Group,*Ph.D. Thesis, University of Waterloo, 2004*On the number of factorizations of a full cycle*, J. Combin. Theory Ser. A, 113 (2006), 1549-1554*Minimal transitive factorizations of permutations into cycles*, Canad. J. Math. (to appear)- (with A. Rattan)
*Minimal factorizations of permutations into star transpositions*, - (with A. Rattan)
*The number of lattice paths below a cyclically shifting boundary*, J. Combin. Theory Ser. A (to appear)

Please contact me if you have any questions or would like further information.