Tom Roby's Math 2710 Home Page (Spring 2013)|
Transition to Advanced Mathematics
Questions or Comments?
COORDINATES: Classes meet Tuesdays and Thursdays
9:30–10:45 in MSB
319. The registrar calls this Section 003.
PREREQUISITES: MATH 1132 or 1152 (first year
An Introduction to Mathematical Thinking Pearson Prentice Hall, 2005.
WEB RESOURCES: The homepage for this course is
http://www.math.uconn.edu/~troby/Math2710S13/. I may list some
SOFTWARE: For generating data to understand properties of
integers, or to solve equations, computer software can be a valuable
tool. Doing some computations by hand is generally good for learning,
but having software that can do bigger computations or check your
work is very useful. One free source on the web
is WolframAlpha. For a
full-fledged programming environment, check out the free open-source
computer algebra system
called Sage. For something free
and easy to use but with more limited capabilities,
GRADING: Your grade will be based on two midterm exams, one
final exam, homework, & in class work (generally on Tuesdays).
The breakdown of points is:
| HW || InClassWork|| Midterms || Final |
|25% ||10% || 20% each ||25% |
MIDTERM EXAMS: Will cover all the material up to that point in
the term. They are currently scheduled for
THURSDAY 28 FEBRUARY 2013 and THURSDAY 11 APRIL 2013
during our usual class meeting.
Please let me know immediately if you have a conflict with those dates.
There are no makeup exams.
HOMEWORK: Homework will be assigned most
weeks, and should be attempted by the following TUESDAY, when I will
be happy to answer questions or provide hints. It will generally be
due Thursdays at the start of class. Since I may discuss the homework
problems in class the day they are due, late assignments will be
accepted only under the most extreme circumstances. (Please let me
know as soon as possible if you find yourself with a situation that
might qualify.) The lowest written homework score will be dropped in
The assignments are listed below in the class
schedule. Sometimes it's just problems from the text, sometimes
there's a handout that includes other problems as well.
You may find some homework problems to be
challenging, even frustrating, leading you to spend lots of time and
effort working on them. This is a natural part of doing mathematics,
faced by everyone from school children to top researchers. I encourage
you to work with other people in person or electronically. It's OK to
get significant help from any resource, but in the end, please write
your own solution in your own words. Copying someone else's work
without credit is plagiarism and will be dealt with according
policy. It also is a poor learning strategy.
ACADEMIC INTEGRITY: Please make sure you
are familiar with and abide by
Student Code governing Academic Integrity in Undergraduate Education
and Research. For quizzes and exams you may not discuss the
material with anyone other than the instructor or offical proctor, and
no calculators, phones, slide rules or other devices designed to aid
communication or computation may be used.
ACKNOWLEDGEMENTS: Many people have
influenced my approach to this material, particularly Arnold Ross and
others with whom I worked in the Ross Program at Ohio State, Hampshire
College Summer Studies in Mathematics, and PROMYS Program at Boston
University. I've also learned much from my UConn colleagues Keith
Conrad, Johanna Franklin, Alvaro Lozano-Robledo, Steve Pon, and Reed
CONTENT: The main learning objective of
this math course is for students to become comfortable reading and
understanding theoretical mathematics, and to gain facility in
constructing their own mathematical arguments. It has many
similarities with a writing course, and I will try to provide for
some work to be rewritten after you have received feedback on it.
ACCESSIBILITY & DISABILITY ISSUES: Please
contact me and UConn's Center for
Students with Disabilities as soon as possible if you have any
accessibility issues, have a (documented) disability and wish to
discuss academic accommodations, or if you would need assistance in
the event of an emergency.
LEARNING: The only way to learn
mathematics is by doing it! Complete each assignment to the best of
your ability, and get help when you are confused. Come to class
prepared with questions. Don't hesitate to seek help from other
students. Sometimes the point of view of someone who has just figured
something out can be the most helpful.
CLASSTIME: We will sometimes spend classtime
doing things in groups, presenting mathematics to one another, or having
interactive discussions. There will not be time to "cover" all material
in a lecture format so you will need to read and learn some topics on
your own from handouts, web sources, or otherwise.
SCHEDULE: The following is a the start of a
tentative schedule that I will update throughout the semester. If
you have a religious observance that conflicts with your participation
in the course, please meet with me within the first two weeks of the
term to discuss any appropriate accommodations.
2710 (STILL BEING REVISED) LECTURE AND ASSIGNMENT SCHEDULE |
|| Logic, sets, quantifiers
|| Proofs & Counterexamples
|| Divisibility & Properties of Z
|| HW #2: Ch. 2 (p.50), #2–30even
|| Division Algorithm & Euclid's Algorithm
|| HW #1 due.
|| Solving Linear Diophantine Equations
|| HW #3:
|| Consequences of Bezout
|| HW #2 due.
|| Going over sample proofs
|| Prime Numbers
|| HW #3 due.
|| Modular arithmetic
|| HW #4: Ch. 2: #70, 72, 93; Ch. 3: #2-10even
|| More mods & equivalence relations;
|| HW #4 due.
|| § 3.5
|| Catchup & Review Day
|| Do Practice Midterm 1 by today
THURSDAY 28 FEBRUARY 2013 MIDTERM EXAM 1 on Chapters
|| Equations in mods; Fermat's Little Thm
|| HW #5: Ch. 3: #22–44even, 56, 68
|| Euler's Thm. and Phi-function
|| HW #5 due
|| Mathematical Induction & Recursion
|| HW #6: Ch. 3: 57,60,61,62,64,97,98,102,104
|| Binomial Theorem
|| HW #6 due
18-22 MARCH SPRING BREAK, NO CLASSES |
|| Rational & Real Numbers
|| HW #7: Ch. 4: #2–12even,28,36,58,65
|| Rational exponents & Decimal expansions
|| HW #7 Due
|| Functions, Graphs, Composition
|| HW #8: Ch. 5: #5,6,7,20,36,37; Ch. 6: #2-8even, 16, 22-34even
|| Inverse functions, Bijections, Cardinality
|| Catchup & Review Day
|| HW #8 due
THURSDAY 11 APRIL 2013 MIDTERM EXAM 2 ON CH. 3–5|
||§ Hndout Ch. 13
|| Limits & Monotone Convergence.
|| HW #9: Ch. 13: 8,10,16,22,25,27,30,32a,34,39
||§ Hndout Ch. 13
|| Decimal Expansions & Uncountability
||§ Hndout Ch. 14
|| Convergent Sequences;
|| HW #9: Due
||§ Hndout Ch. 14
|| Convergent Series
|| HW #10: Ch. 14: #8,9,11,13,18, 36, 47
||§ Hndout Ch. 14
|| Convergent Series
|| Midterm 2 Rewrites due
|| Catchup & Review Day
|| HW #10 due
SUNDAY 5 MAY 2013 5:30-7PM REVIEW SESSION IN MSB 319
THURSDAY 9 MAY 2013 8-10AM: FINAL EXAM IN MSB 319
Conrad has an Expository
paper website with many useful handouts on elementary number
theory and abstract algebra. Some of these give alternate
presentations to some of the topics of this course that some might
A discussion of
Here are some links to examples of proofs both well and poorly written:
- I think that if you use the "manual clickers" more in class
instead of just waiting and waiting for a response from us would be
Thanks for mentioning this. I've tried to use the card clickers more
during the past few lectures and hope this has helped.
- Grader is inconsistent in their grading.
- Time can be spent more wisely, sometimes goes off topic. I am
starting to feel unprepared for the upcoming exam. Would like to see
different proof techniques! More group work! Possibly breaking up
into groups and working collaboratively on a proof with a couple
other people and then comparing and critiquing them as a
class. Grader seems to be a bit inconsistent, maybe you can review
our work after it is graded. Thank you.
Thanks for all this feedback! This is a particularly tricky course to
teach, and I'm still feeling my way with a new book and a somewhat
different approach than I've used in the past. Figuring out how to
balance lecture, group work, etc., is part of that; maybe I can do
more to poll the class about that in the next week or two.
As far as the exam goes, it won't cover anything that you haven't had
time to work through in class and HW. If you are feeling
unprepared in other ways where I can help, please let me know. The
nature of this course is that students need much individual
feedback on their own work, and it's very hard to make that
happen given other constraints on time and departmental resources.
As far as consistency in grading goes, I'm always
happy to take a look at anything you think wasn't graded properly. I
would be love to hear more specifics, which I could then pass back to
the grader while preserving anonymity (if that would help). My
current sense is that the grader takes a good deal of time to write
detailed comments about proofs, and unlike me, her handwriting is
- I enjoy this class a lot. Most professors cover something briefly
in class and expect you to know it in depth, but I feel like you
actually care if we understand the material. I think the most
helpful thing for me would be a practice exam. This would help me
practice the material one last time before the test and give me more
confidence going into it.
Thanks! I hope some of the skills you learn and
practice you get in grappling with mathematical reasoning from this
class will serve you well in future math classes, where the pace will
generally be much faster. I do plan to provide practice exams before
each midterm and the final; thanks for the reminder.
- Please, no more group work than we currently have. The status quo
is fine. Also: I am starting to think your purposeful mistakes
aren't actually purposeful at all...
Thanks for helping me figure out the right balance of
lecture to group work. Today was pretty much all lecture, so I'm not
sure what prompted the comment, maybe last week's looking student
proofs to make improvements? As for my mistakes, I hope that catching
them serves a purpose, even if it was perhaps not my intention at the
time I made them...
- Can we go over #4 and #6 from the hw that is due on thursday? I
don't know how to go about it, but I don't want to ask out loud in
Thanks for mentioning that. I did go over them,
though since we were rushed at the end, I also sent the email on
Wednesday. I also got several email questions about these problems,
which means perhaps there was no need to feel shy about asking?
- I am having difficulty solving problems involving sets and I feel
>like we haven't spent sufficient time on them.
Good point. I took some time today with the set
proof from the HW. Did that help? Most proofs involving sets are long
on technique and short on theory, which makes them less fun for class,
but still important.
- I feel like this course is really similar to a W class in the way
that we spend a lot of time trying to improve our writing. I feel
like exams are not the best way to test our knowledge of the
material. Maybe a packet of proofs to write or some sort of take
home would be better.
There's definitely truth in what you say, and I hope
to write exams where time pressure won't be a major factor. On the
other hand, most math courses for which 2710 is a prerequisite will
have in-class exams, so this course should prepare you for those.
I also think it's important to have samples of students work which
were indisputibly created without any outside help in order to grade
fairly. It's hard to guarantee that with a take-home exam.
- Can we do more examples in class that correspond to the homework? I
feel like the homework asks us to do things that we have yet to learn
and that aren't covered well in the text. Because the homework is
actually graded (and graded strictly), I feel like we should learn more
of how to do the problems it asks us, and those should be what we would
see on the exams anyway, hopefully.
We could, but I think it would be best if the
students in the class took the initiative to ask about specific
HW questions. As you progress to higher levels of math, your
instructors will assume a increasingly greater ability for you to learn
things on your own or from a text. So in this course we start to
transition away from the earlier paradigm of "learning procedures and
practicing them" to "grappling with material you don't understand,
figuring some of it out, and getting help as needed from classmates, the
web, and the instructor." Learning how to ask good questions, i.e.,
trying to pinpoint what might be confusing you, is an important first
step in this process. I'm sympathetic to the challenge, but have
confidence that you can achieve this greater independence (aka
"mathematical maturity"), which will serve you well in math and your
other learning endeavors.
- I really enjoy this class, and think it is taught well! Do you
think you could send us an answer sheet to the practice midterm? I
think it would help to be able to confirm we are doing it correctly!
Thanks for the positive feedback. I've just posted
solutions to the practice midterm. Please keep in mind that there are
often multiple correct proofs or solutions, so don't take mine as
- Will there be rewrites on the exams? I am concerned because our
homework is graded very strictly and exams are worth a large
portion of our grade.
Good question. It's a lot of extra work for the
instructor, but there's definitely some pedagogical value. Generally
I decide case-by-case, based on how the exam, went whether rewrites are
worth the effort. An alternative if the grades seem too low because
the exam was hard is to curve the scores in some way, or add a
constant to everyone's scores. This is much less work (for everyone),
but not as useful for learning.
- I am nervous about the final exam since there will not be any
rewrites! In addition to no rewrites, there is a lot more material
that it will cover than the midterms. I don't want it to have a
huge negative effect on my grade, yikes!
That's certainly understandable. I hope that all
the work of writing and rewriting will pay off by the end of the
term. When creating and
grading the final I take into account the lack of rewrite. Even so
sometimes I misjudge how hard a question will be and am forced to
curve it when everyone does poorly. So as long as your performance on
the final is not significantly lower than others, even if it seems
low in an absolute sense, it shouldn't hurt your grade. Please study
- I really appreciate your passion for teaching! It's encouraging
to know you truly care about your students' success and developing
mathematical maturity. Thank you!
Thank you for such positive feedback! Are you sure
you don't have anything to add? :-)
NEWS & NOTES
Here are some other handouts:
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