Holy Cross Mathematics and Computer Science
MATH 351 -- Modern Algebra I, Fall 2018
Syllabus and Schedule
Information and Announcements
- The final exam for our course will be given in Swords 328 starting at 8:00am on Friday, December,
14. Review sheet; solutions
for review problems.
You will also want to take a look
at the review sheets for the two midterms to prepare:
Examples, Solutions, Class Notes, Etc.
- Our textbook, Abstract Algebra
by Gregory Lee, is available in electronic form as a .pdf file to Holy Cross students at no charge. Let me
know if you have any trouble accessing it.
- Solutions for Midterm Exam I.
- Solutions for Midterm Exam II.
- Solutions for Final Exam.
Assignments
- Problem Set guidelines
- Problem Set 1 -- From Lee: 2.34, 2.36, 2.38, 2.42 (see the statement and proof of Theorem 2.13), 3.2, 3.4, 3.8, 3.16. due: in class on Friday, September 7.
- First Problem Day: Ana Acevedo Soto: 2.33 (there are answers in the back of the book, please show all steps to get them),
Ty Bramer: 3.6, Ryan Ferraro: 3.10. Be prepared to present solutions of these in class on Friday, Sept. 7.
- Problem Set 2 -- From Lee: 3.12, 3.14, 3.18, 3.20, 3.22. 3.26 (Hint: if you fix m, these can be proved by
induction on n, but if you do it that way,
the cases n > 0 and n < 0 must be handled separately for a complete proof). due: in class on Friday,
September 14.
- Second Problem Day: Jinghan Chen: 3.15 -- same question but adding the condition that n ≥ 2,
John Graf: Like 3.23 (1), but for the group Z18, Carrie He: Like 3.23 (2) but for the
group Z3 × Z4. Be prepared to present solutions of these in class on Friday, Sept. 14.
- Problem Set 3 -- From Lee, 3.28, 3.30, 3.32, 3.34 parts (2) and (3), 3.44, 3.46. due: in class on Friday,
September 21.
- Third Problem Day: Katherine Hegermiller: Look at 3.31,
but change the statement to be proved to say "Show that if an abelian group has strictly
more than 3 elements of order 2, then it has at least 7 of them", Jack Hurley: 3.38,
Sophia Lima, 3.40. Be prepared to present solutions of these in class on Friday, Sept. 21.
- Problem Set 4 -- From Lee, 3.48, 3.54, 3.56, 3.60, 4.4, 4.6. due: in
class on Friday, September 28.
- Fourth Problem Day: Marty Murphy: 3.49 (It's OK to consult the solution;
also be able to explain what it means if n = 30), Zakariye Muse: 3.53
(D8 is the group from the example on pages 52 and 53),
Leydi Pliego: 4.2. Be prepared to present solutions of these in class on Friday, Sept. 28.
- Problem Set 5 -- From Lee, 4.10, 4.12 part (2) (part (1) will be done in class), 4.14, 4.16.
due: in class on Friday, October 19.
- Fifth Problem Day: Victoria Roy: 4.7, Casey Sherman: 4.15, Sarah Vrountas: 4.19. Be prepared to present solutions of these in class on Friday, Oct. 19.
- Problem Set 6 -- From Lee, 4.22, 4.26, 4.28, 4.32, 4.40. due: in class on Friday, October 26.
- Sixth Problem Day: Elena Wang: 4.24, Audrey Yang: 4.34. Be prepared to present solutions of these in class on Friday, Oct. 26.
- Problem Set 7 -- From Lee, 4.36, 4.42, 4.44, 4.46, 4.52. due: in class on Friday, November 2.
- Seventh Problem Day: Ana: 4.41, Ty: 4.47, Ryan: 4.49. Be prepared to present solutions of these in class on Friday, Nov. 2.
- Problem Set 8 -- From Lee, 5.2, 5.4, 5.10, 5.12, 5.18. due: in class on Friday, November 9.
- Eighth Problem Day: Damon: 5.3, John: 5.5, Carrie: 5.17. Be prepared to present solutions of these in class on Friday, Nov. 9.
- Problem Set 9 -- From Lee, 6.2, 6.4, 6.10, 6.26 (you'll want to use Lemma 6.2!), 6.28, 7.2, 7.8.
due: in class on Friday, November 30.
- Ninth Problem Day: Kate: 6.17, Jack: 6.19, Sophia: 6.5, Marty: 6.7 Be prepared to present solutions of these in
class on Friday, Nov. 30.
- Problem Set 10 -- From Lee, 7.10 (you may use the Sylow theorems here even though they come later in the book), 7.18, 7.20, 7.22, 7.24, 7.26, 7.30. due: in class on Friday, December 5.
- Tenth and Final Problem Day: Zak: 7.12 (think about the consequences of Lemma 6.2),
Victoria: 7.21, Casey: 7.17, Elena: 7.23, Audrey: 7.33.
Be prepared to present solutions of these in class on Friday, Dec. 7.
Related Links
- Early history of solution of polynomial equations
- Note: The Greek phrase appearing next to the heading of this page is one traditional rendering of
the reported inscription over the entrance to Plato's Academy in Athens
(founded about 387 BCE). It means (roughly) Let no one ignorant of geometry enter.
This is a reflection of the foundational role of geometry in Plato's ideas about knowledge and education.
Downloading Information
The links for assignments and other handouts shown above with the notation
(.pdf file) lead to documents in PDF format.
To
my personal homepage
To the Math homepage
To the Holy Cross homepage
Last modified: December 13, 2018