Foundations of Higher Mathematics
Autumn Semester 2013
Lecturer: Michael Tychonievich
Text: Mathematics 3345 Autumn Semester 2013 by Neil Falkner. This book is required for course readings and homework. Editions as far back as Autumn Semester 2012 are fine, but editions from Spring 2012 or prior may not have the correct text or problems.
Optional Text Message Reminders: Text @math334 to (614) 914-4794 to receive text message notifications through Remind101. I will send out notices whenever I make changes to this website, including but not limited to uploading documents, assigning homework, and scheduling exams. This service is completely optional, and you use it at your own risk; I have no control over what the service may do with your phone information. The homepage for Remind101 is https://www.remind101.com/.
Office hours: MWF 1:00-2:30 PM, and by appointment.
I will have office hours T 12:30-1:30 and 3:00-4:00
Grading: Midterm 1 (up to Section ~5): 20%
Midterm 2 (up to Section ~13): 20%
Final Exam (comprehensive): 40%
Homework and Quizzes: 20%
Current and Upcoming Events:
Final Exam Review Session on 11/18: location CH 312, starting at 5:30PM.
HW 20 (Section 12, exercises 8-11, 13, 15, 19, 23, 24, 29); to be turned in by the start of class on 11/18.
HW 21 (Section 13, exercises 2, 3, 5-11, and prove that any infinite set has a subset equinumerous with the set of natural numbers}; to be turned in by the start of class on 11/25.
Final exam (comprehensive) on the date and at the time determined by the registrar. Sample.
More problems: Section 14, exercises 6-8, 11, 13; Section 15, exercises 1, 2, 5, not to be turned in.
LaTeX Help: Here is a preliminary template to start with when writing up homework in LaTeX. You will need an editor and a compiler to work with this file; WinEdt is a decent combination for Windows users.
Extra Credit Projects. Here is the written extra credit assignment for the course, along with its LaTeX source code if you are interested in using it to aid you in your writeup. It will be worth up to 15 points added to your midterm score, but do note that it is significantly more difficult than all other course assignments, and it will be graded much more harshly. The assignment it to be turned in by 5:00 PM on December 3, either to me at my office or to the front desk of the Math Tower.
You may also perform in-class presentations or organize
review sessions for extra points, again added to your
midterm score. Total extra credit will be capped at 20 extra credit points or 200 total midterm points, whichever is lesser.
I will not consider credit points when I determine grade cutoffs, but I will add them to your score afterwards when calculating your grade.
General course information: The aim of this course is for you to learn the fundamentals of reading and writing proofs. This will involve
learning to write, speak, and even think in a different language, the language of mathematics. I will aid you in this during class, but as with
all languages your learning will come mostly from practice. As such, you should read all assigned reading, and write out proofs from the
book in your own words to make sure that you understand them. I expect you to know key definitions, and to be able to use them in proofs
(in fact, the best way to learn a definition is to use it repeatedly, i.e. to practice). I expect you to do the problems and reading that I assign.
Grading will go as stated above. The exams and quizzes will primarily consist of problems like those done in class, assigned for homework,
and done as examples in assigned reading. I will occasionally ask you to write out definitions from class or from the book. Many problems
will be given in the form of prove or disprove statements, for which you must first formulate a claim, and then give a proof. Homework will
be assigned once or twice a week, and will typically be due three class periods after being assigned. Homework assignments will be added
to this document as they are assigned.
If you want extra help with the homework, please come to my regular office hours as listed above. I may be available at other times, but
you should first confirm with me by email to ensure that I will be free and in my office.
When doing homework problems, it helps to have by your side a list of relevant definitions copied verbatim from the book. Think of it as
a dictionary that will enable you to know the precise meaning of individual terms until you have all of the definitions mastered. When
doing rough work for a problem, you should copy down every definition that seems relevant, and look for connections. Do not despair if the
initial arguments you give are incorrect; it is often less difficult to correct mistakes in rough work than it is to cut new solutions from
When you write up your homework to be graded, you must use complete sentences with proper English grammar (extra consideration
will be given for students for whom English is not a first language). Because you will be writing short technical essays and not just writing
out lists of equations, you should expect to have to revise your work, possibly multiple times. If you decide to write your work up by hand,
please mind your handwriting and margins so that the grader will have no difficulty reading your work. The grader will be instructed to
reject (with a 0) any turned-in assignments that he feels are too sloppy. This includes, but may not be limited to, papers that lack
a student’s name, papers that do not utilize staples to attach multiple sheets together (paper clips and “paper staples” are not good
enough), and papers which still have the chaff left over from being torn out of spiral-bound notebooks.
If you wish to write up your homework with typesetting software, please ask me about it. Typesetting guidelines to be posted. You should
write your homework at a level appropriate for other students in the class. It is not enough to demonstrate to the grader or me that you
understand what you are doing in the problem; you must write proofs that could be understood by another student who knows all of the
appropriate definitions but who is not familiar with your argument. It should be clear what your goal is in a problem without having to
refer to the book; a simple restatement of the problem goes a long way towards this.
When writing proofs, you must know the definitions used precisely. Copy them down exactly from the book and learn them exactly as
written. It is not enough to have a general idea of what a definition says, as at this stage it is easy to change the meaning of a statement
while attempting to paraphrase it.
You are responsible for material as it is covered in class. Taking notes in class will allow you to have a record of this, as well as get you
started on working through the book examples.
If you feel that you may need an accommodation based
on the impact of a disability, you should contact me privately to discuss your
needs. Please contact the Office for Disability Services at 614-292-3307 in room 150 Pomerene Hall to coordinate reasonable accommodations
for documented disabilities.
HW 1 (Section 2, exercises 1-12); to be turned in by the start of class on Friday, 8/30.
HW 2 (Section 2, exercises 14, 15, 17, 19, 20, 22-24); to be turned in by the start of class on Wednesday, 9/4 (no class on Monday, 9/2).
HW 3 (Section 3, exercises 1(e-k), 2-7); to be turned in by the start of class on Monday, 9/9.
HW 4 (Section 3, exercises 9-11, 13, 14); to be turned in by the start of class on Friday, 9/13.
HW 5 (Section 4, exercises 1-7); to be turned in by the start of class on 9/18.
Quiz 1 (Sections 2,3) on 9/18. Sample.
HW 6 (Section 4, exercises 8-14); to be turned in by the start of class on 9/20.
HW 4 Solutions.
HW 7 (Section 4, exercises 15-18, 22-25); to be turned in by the start of class on 9/23.
Quiz 2 (Section 4) on 9/25. Sample.
HW 8 (Section 5, exercises 1-6, and Section 4, exercises 26, 27); to be turned in by the start of class on 9/27.
HW 9 (Section 5, exercises 7-11); to be turned in by the start of class on 9/30.
Midterm 1 on 9/30 in class. Sample.
HW 10 (Section 5, exercises 12-16); to be turned in by the start of class on 10/4.
HW 11 (Section 5, exercises 17-19, 21); to be turned in by the start of class on 10/7.
HW 12 (Section 6, exercises 1-5); to be turned in by the start of class on 10/14.
HW 13 (Section 6, exercises 7-13); to be turned in by the start of class on 10/18.
HW 14 (Section 7, exercises 1-4, 10); to be turned in by the start of class on 10/21.
HW 15 (Section 10, exercises 5, 6, 8-11, 13); to be turned in by the start of class on 10/25.
HW 16 (Section 10, exercises 12, 14-19); to be turned in by the start of class on 10/28.
HW 17 (Section 10, exercises 20, 24, 25, 33); to be turned in by the start of class on 10/30.
HW 18 (Section 11, exercises 4, 5, 12, 15, 20); to be turned in by the start of class on 11/6.
Quiz 3 (Sections 10 and 11) on 11/8. Sample.
HW 19 (Section 11, exercises 22, 23, 25, 26 and Section 12, exercises 1-6); to be turned in by the start of class on 11/13.