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Math 321: Intro to Advanced Math, Fall 2016

Instructor: Dr. William DeMeo
Email: [williamdemeo at gmail]( 321: (insert an informative subject))
Office: PSB 404
Office hours: Tue, Thu 10:30am--12:00pm, PSB 404
Lecture time and location: Mon, Wed, Fri 1:30--2:20pm, Keller 301.

Course Webpage:


Remarks about office hours: The regularly scheduled office hours listed above are subject to change. Changes will be announced during lecture. It is helpful (but not required) to send an email in advance to let the instructor know when you plan to visit.

Table of Contents


You are now reading the main course web page and syllabus for Math 321.

This page will be updated throughout the semester. Students are expected to visit this page periodically.

Textbook Information

We will mainly use the following (required) textbook in this class:

Title: How To Prove It (2nd edition)
Author: Daniel J. Velleman
Publisher: Cambridge University Press
Year: 2006

Students are expected to own (or have access to) a copy of the required textbook, "How to Prove It". It may be possible for some students to get by with just the lecture notes, but that is not recommended.

Here are some other (optional) supplementary textbooks that students might find useful:

  1. Book of Proof by Richard Hammack.

  2. Mathematical Reasoning: writing and proof by Ted Sundstrom.

  3. Mathematical Logic by Stephen Cole Kleene.

The first two of these supplementary books are similar in coverage to "How To Prove It." The third is a more advanced book on logic and foundations of mathematics. It is included in the list because the other books might leave some students unsatisfied, since their primary purpose is to provide a gentle introduction to abstract mathematics, so they carefully avoid overwhelming students with lots of details and technicalities. If you feel unsatisfied and want to learn more of the foundational details, you might find Kleene's book useful.

Overview, Prerequisites, Outcomes

Course Description (from the catalog)
Formal introduction to the concepts of logic, finite and infinite sets, functions, methods of proof and axiomatic systems. Learning mathematical expressions in writing is an integral part of the course.

This course emphasizes the reading and writing of mathematical proofs.

Prerequisites: 243 (or concurrent) or 253A (or concurrent), or consent.

Learning Outcomes

Students will gain proficiency in reading and writing proofs, as well as solving computational problems, concerning the following topics:

See the list of Course Objectives below for more details.

Writing Intensive Aspects of the Course

This class will use writing to promote the learning of course materials and written assignments will contribute significantly to the student's grade. In particular, students will be actively engaged in the reading and writing of formal and informal proofs of mathematical statements. The written work will amount to roughly 4 to 6 handwritten pages per week (equivalently, 2 to 3 typed pages per week).

All of the mandatory writing assignments must be adequately completed in order to pass the course with a 'D' or better. Students who do not complete the mandatory writing assignments will get a D- or an F and will not earn W Focus credit. The types of writing assigned will vary and may include formal and "informal" (writing that is not revised) writing. More details about each writing assignment will be provided in that assignment's description.

Another aspect of the writing component of this course that will be elucidated over the course of the semester is the problem of determining what constitutes a mathematical proof and at what level of detail and formality a proof should be presented. Developing the skills required to determine the appropriate level of detail and formality of mathematical arguments requires a lot of practice and experience and one objective of this course is to give students the opportunity to gain such experience.

Attendance Policy

Students are expected to attend all classes. A grade penalty will be exacted if you have an excessive number of absences (whether excused or unexcused). Specifically, you are permitted (but strongly discouraged from taking) seven absences in total, and you must email the instructor if/when you must miss a class. Each additional absence, and any absence not mentioned to the instructor, may result in the deduction of points from your final grade.

Occasionally attendance will be recorded by passing around a sign-in sheet on which you will print and sign your own name. If another student asks you to sign in for them, don't do it! Forging another student's signature constitutes a violation of the student code of conduct and will be referred to the UH Office of Judicial Affairs.

Important: If you plan to leave before class is over, the correct procedure is to mention this to the professor before the start of class. It is impolite and disruptive to your classmates to leave, or even pack up your belongings, before the lecture is over.

Grading Policy

The breakdown of the final course grade is as follows:

  • Homework: 40 points total
  • Two midterm exams: 30 points (15 each)
  • Final exam: 30 points

At the end of the semester, letter grades will be assigned roughly according to the following table. However, the scale may be shifted depending on overall student performance.

  • A: 94--100
  • A-: 91--93
  • B+: 87--90
  • B: 84--86
  • B-: 81--83
  • C+: 77--80
  • C: 74--76
  • C-: 71--73
  • D+: 67--70
  • D: 64--66
  • D-: 60--63
  • F: 0--59


There will be two midterm exams each worth 15%, and a final exam worth 30% of the course grade.

  • MIDTERM EXAM 1 covering chapters (tbd)
    DATE: Friday, October 7
    TIME: 1:30--2:20pm
    LOCATION: Keller 301

  • MIDTERM EXAM 2 covering chapters (tbd)
    DATE: Wednesday, November 23
    TIME: 1:30--2:20pm
    LOCATION: Keller 301

  • FINAL EXAM (cumulative)
    DATE: Monday, December 12, 2016
    TIME: 2:15--4:15pm
    LOCATION: Keller 301

In accordance with university policy, the final exam is mandatory and must be taken by all students at the scheduled time. Do not make travel plans before the date of the final exam.


Late homework will not be accepted or graded.

The homework will account for 40% of the course grade and will be assigned every other week, typically due on Wednesday at the beginning of class.

You must submit a hard copy of your homework. Electronic documents (e.g., email attachments) are not acceptable.

Homework submitted at the end of class on the due date will be penalized 10%. Homework submitted after then end of class on the due date will not be accepted or graded. The lowest (or missed) homework score will be dropped and not counted toward the final course grade.

Descriptions of each homework assignment will be available in the homework directory of this repository. Homework is due in class on Wednesday two weeks after it is assigned.

This is a writing intensive course, so you will be graded both on the correctness of your solutions, and also on the quality of your writing. You will get the graded homework back in class on the Friday after it is due. At this point, you will have until the next Wednesday (five days) to do corrections for 2/3 of the original credit. You may only do corrections on problems that you have made a 'reasonable' first attempt at, so please try to do everything the first time around!

You are strongly encouraged to start the homework early, and to come to me if you have any questions.

Make-up Policy

No late homework will be accepted for any reason. If you fail to submit homework on time, this will not necessarily hurt your course grade since the lowest homework scores will be dropped.

Generally speaking, there are no make-up exams. However, if you must miss an exam for one of the legitimate reasons listed below, and if you contact the professor at least five days before the exam date, then you might be able to take a make-up exam before the scheduled exam time.

To request a make-up exam, a student must provide documented evidence of one of the following:

  • Documented medical excuse - student's own medical emergency.
  • Documented medical excuse - a member of the student's family has a medical emergency.
  • Extra curricular activities as a representative of University of Hawaii.
  • Armed forces deployment (military duty).
  • Officially mandated court appearances, including jury duty.
  • A conflict with another exam or if you have three or more final exams on a given day. (In each case the exam with the fewest students must arrange the make-up exam.)

If you miss an exam due to some unforeseen circumstance, you must contact the professor within one class meeting after the missed test and provide an explanation. If your excuse is accepted, the missed test score may be replaced with 80% of your final exam score. For example, if your excuse is accepted and you score a 90% on the final, then you will receive a 72% for the missed test (0.80*0.90 = 0.72).

Asking Questions

Students are strongly encouraged to ask lots of questions. If you don't understand something, please ask!

  1. In Lecture. The best time/place to ask a question is during lecture or recitation or office hours.

  2. On Piazza. Another good place to ask a question is the online discussion forum. This term we will be using Piazza for class discussion and all students should enroll in this forum by visiting the Piazza signup page.

    This system is highly catered to getting you help fast and efficiently from classmates and the professor. Rather than emailing questions to the teaching staff, students are encouraged to post questions on Piazza forum. If you have any problems or feedback for the developers, email

    The Piazza page for this class is

Email Policy

You may email the instructor directly, though the response time might be a slower than if you use one of the preferred methods described above.

If you email the instructor, you must use an informative subject field. If you use this link to email the professor, then some of the required information should pre-populate your message fields. If you do not at least indicate which class you are in, your email might go unanswered.

Classroom Policy and Code of Conduct

Students must abide by the university's student conduct code. In particular, cheating is unacceptable and will not be tolerated. Violations of this policy will be referred to and dealt with by the UH Office of Judicial Affairs in a manner consistent with university regulations, which range from a warning to expulsion from the university.

Use of Electronics During Lecture

Silence and refrain from using all electronic devices (phones, ipods, tablets, microwave ovens, etc.) during class and exam periods. Using a computer during lecture to check Facebook, for example, is totally unacceptable. Besides how this affects your own ability to focus on what is being taught in the lecture, computers can be very distracting to other students. Use of electronic devices in lecture for purposes unrelated to math will not be tolerated.

Students With Disabilities

Students who have a documented disability, or who believe they have a disability that qualifies under the Americans with Disabilities Act and Section 504 of the Rehabilitation Act and requires accommodations, should contact the Kokua office for students with disabilities.

KOKUA Program
Queen Lili'uokalani Center for Student Services 013
2600 Campus Road
Honolulu, Hawaii 96822

Phone Numbers (Voice/Text):
QLCSS building
(808) 956-7511
(808) 956-7612
Fax: (808) 956-8093
E-mail: kokua at hawaii dot edu
Office Hours: Monday--Friday 8:00am--4:00pm

Students must have their paper work in order and must contact the instructor early in the semester so that their learning needs may be appropriately met.

Your instructor will be happy to assist with accommodations, but will not provide them retroactively, so the appropriate requests and paperwork should be filed well before the first exam.

More information about disability resources in the Mathematics Department can be found at

Additional Resources


Introduction to Advanced Math, Fall 2016, University of Hawaii






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