Week of January 21 - 23, 2004
Assignments Made on:

Wednesday (Jan 21) Read: Section 1.1 Mathematician of the Day: Simon Stevin

Friday (Jan 23) Study: Section 1.1 Read: Section 1.2 for Monday Mathematician of the Day: Sir William Rowan Hamilton Assignment 1

Week of January 26 - 30, 2004
Assignments Made on:

Monday Study: 1.2. We will continue with this section in class on Wednesday, in a Group Discussion. Mathematician of the Day: John Coates, who was Andrew Wiles' PhD thesis advisor, and whose birthday is today. :-)

Wednesday Study: Section 1.2 Read: Section 1.3 for Friday. Mathematician of the Day: Eduard Kummer, who in 1843 discovered ideal theory when figuring out what was wrong with attempts to prove Fermat's Last Theorem! Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour (yes, we have Rush Hour again!)... Make a bookmark for our course homepage for future reference. Here you will find all of the general information about the course, including information about exams, homework, grades, etc. All future assignments will be posted to our web site (as .pdf files), and will not be handed out in class. You will need Adobe Acrobat Viewer to download and read these files. If you have any problems with this, please let me know immediately.

Friday Announcement: Group Discussion 1 is due on Wednesday 2/4, not Monday 2/2. Study: 1.3. Read: 1.4 for Monday Mathematician of the Day: Hermann Grassmann, who in 1844 wrote Die lineale Ausdehnungslehre ("Theory of Linear Extension"). In this work, subspaces of a vector space were first represented by coordinates. Grassman's work appears today in some of the structures of differential geometry. Assignment 2, due Friday, February 6.

Week of February 2 - 6, 2004
Assignments Made on:

Monday Study: Section 1.4, on linear dependence and linearly dependent sets. Read: Section 1.4 on linear independence for Wednesday. Mathematician of the Day: Josiah Willard Gibbs, an American mathematician who was a longtime professor at Yale. He developed much of vector analysis as we know it, and used vector methods to simplify methods for finding the orbit of a comet, in 1880.

Wednesday Study: Section 1.4 Read: Section 1.5 for Friday. Mathematician of the Day: August Mobius, who in addition to doing some cool mathematics, studied astronomy under Gauss. In 1858 Mobius discovered properties of 1-sided 2-dimensional surfaces which we now call Mobius strips. Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday CLASS CANCELLED. Read: 1.5 for Monday. Today's definitions quiz: will be given on Monday.

Week of February 9 - 13, 2004
Assignments Made on:

Monday Study: Section 1.5, on solving systems of linear equations. Mathematician of the Day: Nobody new for today! Re-writes for Assignment 1: Here is a chance to "buy back" some points on this assignment! I will accept re-writes for the following problems by the end of the day on Friday: Section 1.1: #12. Section 1.2: #4, 12, 14, 15. You may choose to do any/all/none of these. For each problem, you may earn back up to the number of points you lost on the problem. Please attach your original solutions (or a photocopy) to your rewrites. Solutions for Assignment 1: will be available at the end of this week. Assignment 3: will be posted on Wednesday 2/11, due Wednesday 2/18.

Wednesday Study: Section 1.5 Read: Section 1.6, on "bases" for Friday's class. Definitions Quiz 3: this Friday, at the beginning of class. All definitions up to and including echelon form are fair game. Assignment 3 (due Wednesday February 18th): Section 1.5: 1ade, 2cd, 3ae, 5ac, 6 Supplementary Exercises (p. 59): 1aefgj, 10. Mathematician of the Day: Rafael Bombelli, the "inventor" of complex numbers (depending on who you read). He was the first to describe how to work with them algebraically, in his book Algebra, published in 1572. Our M.O.D. today is in honor of the Job Talks this week and next, some of which are on the subject of complex analysis. Job Talks: On Thursday 2/12, Friday 2/13, and Tuesday 2/17, we will have presentations from our three candidates for the new position in mathematics. Talks are at 4pm in Swords 359, with refreshments in the Swords Lounge at 3:30. Please see the flyers around the department for titles and descriptions of the talks. BONUS OPPORTUNITY: If you come to a talk and submit to me by Wednesday 2/18 a short summary of your impressions of the speaker and the content of the talk, I will give the following bonuses: 5 points added to your HW total, for one talk, OR 10 points added to your HW total, for two talks, OR 5 points added to your HW average for all three talks. Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday Study:1.6, definition and examples of a basis for a vector space. Read: 1.6, which we will continue with on Monday. Mathematician of the Day: nobody new today.

Week of February 16 - 20, 2004
Assignments Made on:

Monday Study: 1.6, theorems concerning bases for vector spaces. Read: material in 1.6 on "dimension" of a vector space. We will discuss this on Wednesday. Mathematicians of the Day: Steve Levandosky, Brent Carswell, and Rachel Weir. (See note on Job Talks in last Wednesday's entry.) EXAM 1: will be held on Tuesday, February 24th, 7-9pm in Swords 328. (Note that this is not our usual classroom.) I will make up the exam as if it were being given in the usual class period, but you may use as much of the two-hour time period as you need. Reminders: Assignment 3 is due in class on Wednesday. Also, since we aren't having our exam this Friday, we will have our usual Definitions Quiz at the beginning of Friday's class.

Wednesday Study: 1.6 on basis and dimension. Be sure to work through and understand the proof of Theorem 1.6.10, which was stated at the end of class today. (The theorem from which we got our corollary about any basis for a given vector space being the same size.) Read: your definitions, in preparation for Friday's Definitions Quiz. Exam 1: will be held Tuesday, February 24th, 7-9pm in Swords 328. Exam Review: will be held Sunday, February 22nd, 7-8:30pm in Haberlin 412. Mathematician of the Day: Augustin Cauchy, who was responsible for many important results in complex analysis. Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday Study: Today's group discussion questions (due on Friday, February 27th). Read: Section 2.1, for Monday. Group Discussion 2, due in class on Friday, February 27. Mathematician of the Day: nobody new today

Week of February 23 - 27, 2004
Assignments Made on:

Monday Reminder: Exam 1 is Tuesday, February 24, 7-9pm, in Swords 328. Study: Section 2.1, on linear transformations. Read: Section 2.2, for Wednesday. Mathematician of the Day: Evariste Galois, a very original thinker. His work on the question of solvability by radicals has become Galois theory (which some of you may study in Math 352 in a couple of years). Galois untimely death came as the result of injuries sustained in a duel!

Wednesday Study: Section 2.1, on linear transformations. Read: Section 2.2, on using matrices to represent linear transformations. Assignment 4 (due Friday, March 5th): Section 1.6: # 2be, 5, 7a, 12, 14c (part a was done in class and will be useful), 15b. Section 2.1: # 3ad, 4, 10, 11, 12ab (and read part c). Section 2.2: # 3ac. As announced in class today, you may not exercise your "late" option on this assignment, since the following week is spring break. Reminder: Group Discussion 2 is due on Friday. Also, office hours tomorrow will be in the evening, 6:30 - 7:30pm, instead of the usual morning hours. Mathematician of the Day: John Conway, who has worked in several fields of math including algebra, number theory, knot theory, game theory, and geometry. Conway's analysis of games runs from the very complicated (Go) to the very simple (Dots and Boxes!). He is the author of several very reader-friendly books which showcase math's fun side. :-) Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday Study: 2.2, on the matrix of a linear transformation Read: 2.3 for Monday Mathematician of the Day: Manjul Bhargava, a rising superstar in number theory, at Princeton University. He proved the Fifteen Theorem for quadratic forms, a result originally proven by Conway but never written up for publication! (Bhargava's solution is more elegant and has gotten quite a bit of attention.)

Week of March 1 - 5, 2004
Assignments Made on:

Monday Study:2.3 on kernel and image of a linear transformation. Read: about the Dimension Theorem, in section 2.3. Mathematician of the Day: John Pell, the British mathematician for whom the Pell equation is named (possibly erroneously?).

Wednesday Study: 2.3, all. Read: 2.4 for Friday Reminders: Assignment 4 is due on Friday. There will be a definitions quiz on Friday, at the beginning of class. Mathematician of the Day: Tom Hull, a mathematician at Merrimack College (in Andover, MA) who is also a master origamist. Try folding 30 of the PHIZZ units and putting them together to make a dodecahedron. Can you do it so that at each place where 3 units meet, you have one of each color? Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday Study: Applications of the Dimension Theorem to properties of linear transformations (invectivity and surjectivity). Read: Section 2.4. Assignment 5 (due Friday, March 19th): Section 2.2: 9ab, 12, 13, 14b (you did part (a) as Problem 14c in 1.6), 15 (the restriction of T:V --> V to a subspace W just means use the same mapping as it applies to the elements of W. Section 2.3: 1bc, 3c, 7, 8, 13, 14. Section 2.4: 1abc. Mathematician of the Day: Sophie Germain, a pioneer in a time when women were {\em not} part of the mathematical community. Sophie corresponded with such luminaries as Legendre and Gauss, under the pseudonym "M. LeBlanc." Her work includes crucial contributions to the progress on proving Fermat's Last Theorem.

Week of March 8 - 12, 2004
Assignments Made on:

Monday No class - SPRING BREAK!

Wednesday No class - SPRING BREAK!

Friday No class - SPRING BREAK!

Week of March 15 - 19, 2004
Assignments Made on:

Monday Study: Section 2.4. Read: Section 2.5. Bonus Opportunity: The Math/CS Club is the host for this term's Hogwarts at Holy Cross event, which is being held on Friday, March 19th at 6:30pm in the Hogan Ballroom. If you help out with the preparations for the event (making posters, etc.) and/or help staff the event on Friday, you will receive 5 bonus points added to your best exam score in the course. Please see one of the Math Club officers for more details. Mathematician of the Day: Albert Einstein, as yesterday was the 125th anniversary of his birth! Also, for a list of cool quotes by Einstein, click here.

Wednesday Study: The applications of the dimension theorem that we've proved in the past two classes: Proposition 2.4.2 and its corollaries, Proposition 2.4.7 and its corollaries, and Proposition 2.4.10. Read: The rest of section 2.4, and section 2.5. Next week: There are some changes to the usual schedule: Prof. Frechette will be away at a conference (the Automorphic Forms Workshop). Prof. Damiano will teach our class on Monday and Wednesday. The next homework assignment will be given out on Monday, March 22nd and will be due on Monday, March 29th at the end of the day. Office hours will be held Friday March 26th 2:30 - 4pm, and Monday March 29th 10-11am and 2:30-3:30pm. The date for Exam 2 has been changed. Exam 2 will be given on Tuesday, March 30th, 7-9pm, location TBA. Mathematician of the Day: Physicist John Heighway, the originator of the paperfolding fractal known as "Heighway's Dragon." For some fun information on this, check out Dragon Curves. Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday Study: The material in section 2.4 on particular solutions and general solutions to systems of equations. (This starts with Corollary 2.4.17, and goes through the end of the section Read: Sections 2.5 and 2.6. Next week: There are some changes to the usual schedule. Please scroll up to Wednesday's entry to read about them, if you weren't in class on Wednesday. Bonus Opportunity: The Math/CS Club is the host for this term's Hogwarts at Holy Cross event, which is being held TONIGHT March 19th at 6:30pm in the Hogan Ballroom. If you help staff the event (or you attended one of the prep sessions to help make posters, etc.), you will receive 5 bonus points added to your best exam score in the course. Please see one of the Math Club officers for more details. Mathematician of the Day: Christian Goldbach (1690 - 1764), who is best remembered for his conjecture that every even integer greater than 2 can be represented as the sum of two primes. He wrote this conjecture in a letter to Euler in 1742, and it is still an open question (i.e. unsolved). For info about Goldbach's Conjecture and other unsolved problems relating to prime numbers, check out the Prime Pages.

Week of March 22 - 26, 2004
Assignments Made on:

Monday Study: Section 2.5, on composition of linear transformations. Read: Section 2.6, on invertible linear transformations. Assignment 6 (due Monday, March 29th): Section 2.4: #2bcd, 4acd, 11 Section 2.5: #1c, 2, 5abef, 12, 13 This assignment is due by the end of the day on the 29th. Mathematician of the Day: Guest lecturer, Prof. Damiano!

Wednesday Study: Section 2.5, on the matrix of a composition of linear transformations. Read: Section 2.6, for Friday's class. Mathematician of the Day: guest lecturer, Prof. Damiano! Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday Study: Section 2.6, on isomorphisms between vector spaces. Read: Section 2.6, on finding the matrix for the inverse of a linear transformation. Mathematician of the Day: nobody new today. Review sheet for Exam 2.

Week of March 29 - April 2, 2004
Assignments Made on:

Monday EXAM 2 DATE CHANGE: Exam 2 will now be given on Thursday, April 1st, 7-9pm, room location TBA. Please note the change! Study: Sections 1.6, and 2.1 -- 2.5, for Thursday's exam. Read: Solutions to Assignments 4 and 5. Mathematician of the Day: Benoit Mandelbrot, a pioneer in the subject of fractal geometry. For some fun with the Mandelbrot set, one of the most famous fractals of all, check out The Mandelbrot Set Explorer at the Boston University Dynamical Systems and Technology Project's home page.

Wednesday Study: 2.7, on how to use change-of-basis matrix to change coordinate vectors from one basis to another. Read: 2.7, on how to use change-of-basis matrices to change the matrix of a linear transformation from one pair of bases to another. Reminder: Exam 2 will be held tomorrow evening, April 1st, 7-9pm, in Swords 359. Mathematician of the Day: Waclaw Sierpinski. Known for his work in set theory, among other subjects. The Sierpinski Triangle is one example of a fractal. Check it out! Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday Study: Section 2.7, on how to use change-of-basis matrices to change the matrix of a linear transformation T: V --> V from one basis to another. Read: Section 3.1, on the determinant. Group Discussion 3, from today's class. This assignment is due on Wednesday, April 7th. Mathematician of the Day: nobody new today. Monday's Colloquium: attending, and writing up your impressions of the talk (1-2 paragraphs) will earn 5 bonus points added to your homework total.

Week of April 5 - 9, 2004
Assignments Made on:

Monday Study: Section 3.2 Read: Sections 3.1 and 3.2. We will not be discussing 3.1 in class, but it provides some motivation about the concept of determinants. Assignment 7, due on Friday, April 16th. Mathematician of the Day: Niels Henrik Abel, for whom abelian groups are named. Colloquium today!: "The Geometries of Escher," a talk by Susan Goldstine from Amherst College. Refreshments at 3:30pm in the Swords Faculty Lounge, followed by the talk at 4:00pm in O'Neil 112. Attending, and writing up your impressions of the talk (1-2 paragraphs) will earn 5 bonus points added to your homework total. Please turn in your write-ups on Wednesday.

Wednesday Study: Read: Mathematician of the Day: Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday No class - EASTER BREAK!

Week of April 12 - 16, 2004
Assignments Made on:

Monday No class - EASTER BREAK!

Wednesday Study: Chapter 3, sections 2 and 3, on determinants. Also, study for Friday's definitions quiz. Read: Section 4.1. Mathematician of the Day: Olivia Frechette, age 5, who can count and recognize the numbers from 1 to 100. :-) Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday Study: Section 4.1, on eigenvectors, eigenvalues, and eigenspaces. Read: Section 4.2. Mathematician of the Day: Gotthold Eisenstein, who made major contributions to algebra and number theory. One fact you may have seen which is due to Eisenstein is the following Eisenstein's Criterion. Let p is a prime, and suppose f(x) = a_n x^n + ... + a_0 is a polynomial with integer coefficients such that p divides all the coefficients except a_n, and p^2 does not divide a_0. Then f(x) cannot be factored as a product of polynomials of lower degree with rational coefficients. Monday's Colloquium: attending, and writing up your impressions of the talk (1-2 paragraphs) will earn 5 bonus points added to your discussion total.

Week of April 19 - 23, 2004
Assignments Made on:

Monday Read: Section 4.2, on Diagonalizability Assignment 8 (due Monday, April 26th): Section 4.1: #1, 2, 3acg, 5, 7, 14, 15. Section 4.2: #1ab, 2, 3, 6, 8. NOTE: This is the last assignment that will be collected. Practice problems will be assigned on future topics, for preparation for exams, but they will not be collected. Mathematician of the Day: nobody new today

Wednesday Study: Section 4.2, on Diagonalizability. Read: Section 4.3, on the Geometry of R^n Mathematician of the Day: Piero della Francesca, one of the most influential Italian painters of the Renaissance, and one of the originators of the method of perspective in drawing/painting. Event: Tea & Games, 2-4pm in the Swords Student Lounge. Drop by for some hot chocolate and a game of Abalone, or Set, or Rush Hour!

Friday Study: Section 4.3, on Inner Products and the Geometry of R^n. Read: Section 4.4, for Monday's class Group Discussion: Write-ups for today's discussion are due in class on Friday, April 30th. Exam 3: will be given on Monday, May 3rd, 7-9pm, Room TBA. A review sheet will be handed out in class this coming Monday. The exam will cover material from 2.6 -- 2.7, 3.2, and 4.1-4.3. Mathematician of the Day: David Hilbert, for whom certain inner product spaces known as Hilbert spaces are named. Constance Reid wrote a great biography of Hilbert. One interesting tidbit of information in the book is about his outdoor blackboard. Hilbert liked to work outside, so he put up a blackboard under a covered walkway. When he needed time to think about a problem, he'd leave the board, go ride his bicycle around the yard, and then come back when he had a new idea!