University of Massachusetts, Amherst
Math 300
Fundamental Concepts of Mathematics
Spring 2005
Review Sessions for Final Exam Monday and Tuesday in 1634 LGRT
Click here to go the Homework Page
Click here to go the list of TA sessions
(not the most up to date list)
Course News: You can improve your score for Exam 1 by
following these steps: Step 1. Solve all problems on the exam that
you missed (including Definitions and short answer), seeking help from
me, the TAs or other students. Step 2. Schedule a 15-minute
appointment with me sometime before Exam 2: I will ask you to answer
questions from the test on the board. You will earn a minimum of 5
extra points for doing this. Depending on how well you answer the
questions on the board, you may earn as much as (100-x)/2 more points
where x is your current score. So, if you got a 60, you will be able
to improve
your score to something between 65 and 80 by following these steps.
The final exam is scheduled for May 18, 10:30 am,
in LGRT 101 and 103.
Meeting times: Tuesdays and Thursdays, 11:15-12:30, in Lederle
321. Additionally, during the first week of class, students will be
assigned to a one-hour per week TA session with one of the four
undergraduate TAs. You should make every attempt to attend your own
TA session, but if for some reason, you miss your TA session, you
should feel free to attend another one that week instead.
Instructor: Farshid Hajir
Office: Lederle 1118
Phone: 545-6015
Email: hajir@math.umass.edu
Graduate TA:
Molly Fenn
Office: Lederle
1323 D
Email: fenn@math.umass.edu
Undergraduate TAs:
Laura Beltis, lbeltis@student.umass.edu,
Garret Cahill, gcahill@student.umass.edu,
Anna Derby, aderby@student.umass.edu,
Aaron Wolbach, aaron.wolbach@comcast.net,
Office Hours: Office hours will be held in the Blue Wall on
Wednesdays from 10 until 4.
The staffing is as follows but is subject to change: 10-11
Farshid, 11-12 Garret, 12-1 Molly, 1-2 Anna, 2-3 Aaron, 3-4 Laura.
Stay tuned for any
changes that might occur. For the first few weeks, I will
have a departmental meeting to attend 11-12, but once that is over,
I will also be available in the Blue Wall 11-12.
How often do you take a course where there
are SIX qualified people sitting in the Blue Wall twiddling their
thumbs waiting to help you grasp the (admittedly) difficult material?
If, occasionally, you need help but cannot attend the Wall-to-Blue-Wall
office hours, please contact one of us for an appointment.
Take-home message: show up to the office hours; or else I'll
end up eating too much greasy food and knocking my cholesterol way
through the roof.
Texts: A packet of notes, written by Bill Meeks, will be
provided on the first day of class.
We will also use How to Read and Do Proofs by D. Solow, Fourth Edition, Wiley, 2005. Most homework
assignments will also have a few pages of notes attached. Finally,
it is possible that lecture notes will be posted to this web
site at some point in the future.
Quizzes: Quizzes may be given by the TAs during discussion
sections or by Farshid during lecture; they will probably not be
announced ahead of time. They will consist of one or two very simple
questions.
Philosophical
Remarks: They became so numerous, they lobbied successfully for
their own page.
Homework: Homework will be posted on The
Homework Page and collected every Thursday at the beginning of
lecture. Late homework will not be accepted and the lowest homework
grade will be dropped. Be sure to read and follow the homework
rules.
Attendance: Attendance is required both during lectures and at
the discussion sections. The instructors of the course consider
attendance AND participation important ingredients for your success in
the course. Frequent absences will be reflected in your
grade.
Extra Credit:
Some extra credit problems will occasionally be posted here or given during
class. Each may be worth differing
numbers of points and the student with the most points at the end of the
semester wins a fabulous prize.
Grading:
homework, quizzes, participation - 30%
2 midterms - 20% each
Final exam - 30%
Tentative Class
Schedule:
Week 1 (1/27): Introduction to problem solving and proofs, scheduling of
TA sessions
Week 2
(2/1, 2/3): Reasoning methods, what is a proof and why do we need it?
Week 3
(2/8, 2/10): introduction to set theory, unions and intersections of sets
Week 4
(2/15, 2/17): sizes of sets, countable and uncountable sets
Week 5
(2/22, 2/24): 1-1 and onto functions, equivalence relations;
Week 6
(3/1, 3/3): truth tables, implications, and proofs
FIRST MIDTERM EXAM ON 3/3
Week 7
(3/8, 3/10): well-ordering principle and induction
Spring
Break 3/12-3/20 No Math 300 this week? Woohoo!
Week 8 (3/22,
3/24): More induction and some paradoxes
Week 9 (3/29,
3/31): Real and complex numbers
Week 10 (4/5,
4/7): introduction to group theory, definitions
Week 11
(4/12, 4/14): examples of groups; SECOND MIDTERM EXAM ON
4/14
Week 12
(4/19, no class on 4/21—Monday schedule): properties of groups and subgroups
Week 13 (4/26,
4/28): Lagrange’s Theorem
Week 14
(5/3, 5/5): homomorphisms, kernel, and image
Week 15
(5/10, 5/12): isomorphism theorems and quotient groups
Special Dates:
Wed. January 26, First day of classes
Tues. February 8, Last day to drop with no record
Mon. February 21, Holiday-Presidents’ Day
Wed. February 23, Monday class schedule
Sat. March 12, First day of spring break
Mon. March 21, Classes resume
Wed. March 23, Last day to drop with a ‘W’
Mon. April 18, Holiday-Patriot’s Day
Thurs. April 21, Monday class schedule
Thurs. May 12, Last day of classes
Sat. May 14, Final exams begin
Fri. May 20, Last day of finals