**Mathematics 3345**

**Foundations of Higher Mathematics**

**Autumn Semester 2013**

**Lecturer:** Michael
Tychonievich

**Email:**
tycho@math.osu.edu

**Office:** MW629

**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)
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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
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**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.

**Midterm 2** (Sections 10-13) on 11/22. Sample. Actual test questions.

**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

whole cloth.

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**** studentÕs name, papers that do not utilize staples to
attach multiple sheets together (paper clips and Òpaper staplesÓ 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
specific*

**needs.
Please contact the Office for Disability Services at 614-292-3307 in room 150 Pomerene Hall to coordinate reasonable accommodations **

**for
documented disabilities.**

**Past Assignments:**

**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.