Math 321(W), Introduction to Advanced Mathematics

Instructor: Pavel Guerzhoy

The class meets Tuesdays and Thursdays, 10:30 - 11:45am at 404, Keller Hall.

Office: 501, Keller Hall (5-th floor)
tel: (808)-956-6533
e-mail: pavel(at)math(dot)hawaii(dot)edu (usually, I respond to e-mail messages within a day)
Office hours: Tuesdays and Thursdays 12:00-1:30 and 3:00-4:00pm
General Expectations
The Department of Mathematics has a general expectations statement, which we are assumed to follow in this class.
In this class we use the book
  • Chapter Zero, Fundamental Notions of Abstract Mathematics , 2nd edition, by Carol Schumacher, Addison-Wesley, 2001.
    The book is really unavoidable, and cannot be replaced with another textbook!


    Due Thursday, Dec 17

    Course Objective
    The primary goal of this class to develop a way to approach mathematics as professional mathematicians do. Most of the previous mathematical experience of the students is related to Calculus classes. These classes are primarily directed to acquisition of tools. For this reason, although very useful, Calculus classes tend to create a misleading impression about mathematics. In this class we will learn that mathematics is not about specific tools, but about ideas and arguments. These ideas and arguments are frequently expressed as proofs . The class is designated as writing-intensive. As a consequence, mathematical writing, and particularly, the writing of clear and correct proofs is a subject of emphasis. Several topics from the textbook will be covered. These topics are of substantial importance for most upper division courses.
    Calculus Math243 or Math253A (or concurrent) or consent.

    Grading Policy
    The course contains a combination of concepts, ideas and techniques which the students must be able to apply in solving specific problems. Most of these problems require proving or disproving a certain statements. Since this is a writing-intensive class, we simultaneously learn how to write mathematical texts.

    At the end of the day, your grade will reflect your ability to solve specific problems. This assumes your ability to write down a simple proof so that it is mathematically and grammatically acceptable. More specifically, the following rules are to be taken.

  • Final exam will count for 30% of the final grade. The exam is cumulative (it covers all the material).
      The final exam will be a "take home" exam (you may choose to call it "final paper"). The assignment will be distributed approximately a week before the end of the semester. There will be no make-ups for the final.

  • Six writing homework assignments count together for 40% of the final grade.
      It will be possible to make up these assignments. Moreover, it is recommended to redo them until a certain level of quality is achieved.

  • Midterm test counts for 30% of the final grade. This is a "take home" test. The assignment is possibly as scheduled below.
      In general, there will be no make-ups for the midterm.

    Contents and regular Homework assignments

    This table is approximate, and will be updated regularly.

    An example of how to read the table.
    • Tuesday, 8 Sep is the due date for the writing assignment, and you have to submit your solutions of exercise 3 on p. 64.
    • On Tuesday, 8 Sep we covered Chapter 4.1 in class.
    • For Tuesday, 11 Sep your assignment is to work out problem 4.1.10 on p. 68.
    Remark on the homework. The book contains Theorems, Problems, Exercises without proofs and solutions. The regular homework assignment usually is to work out those of them which are not done in class. Although these assignments are never collected and graded, it is highly recommended to take them seriously. Without doing them a student probably fails to acquire necessary skills, and, as a consequence, fails to do the graded assignments and tests.

    Date Sections Homework Assignment Writing Homework Assignement
    Tue, 25 Aug Ch. 1
    Thu, 27 Aug Ch. 1 7 on p.38; Ponder Q., p.38 1,2,3,6
    Tue, 1 Sep Ch. 2 4,5 on p.54
    Thu, 3 Sep Ch. 3 3.2.3,3.2.4,3.2.5,3.2.6
    Tue, 8 Sep Ch.4.1 4.1.10
    Thu, 10 Sep Ch 4.3 3 on p.64
    Tue, 15 Sep Ch. 5.1,5.2,5.3 5.1.10, 5.1.12, 5.2.2, 5.3.9, 5.3.10
    Thu, 17 Sep Ch. 5.5 5.5.2,5.5.3,5.5.4,5.5.14, 1,2 on p.130
    Tue, 22 Sep Ch. 6.1,6.2 6.2.18, 1 on p.155
    Thu, 24 Sep Ch. 6.3,6.4
    Tue, 29 Sep Ch. 6.5 6.5.4
    Thu, 1 Oct Ch. 6.6,6.7 6.6.6,6.7.3
    Tue, 6 Oct review
    Thu, 8 Oct Ch 7.1,7.2 7.1.6,7.1.8
    Tue, 13 Oct Ch. 7.3 7.3.3
    Thu, 15 Oct Ch. 7.4 7.4.4,7.4.5,7.4.6 7.2.5
    Tue, 20 Oct Ch. 7.5 7.5.7 7.3.5
    Thu, 22 Oct review
    Tue, 27 Oct review 7.5.7, 7.5.8
    Thu, 29 Oct Ch.8.1,8.2 8.2.6 midterm: problems 1 - 7 (all) on p. 176
    Thu, 3 Nov Ch. 4.2,8.3, 8.3.13
    Thu, 5 Nov Ch. 8.4 8.4.11,8.4.12
    Tue, 10 Nov Ch. 8.5 8.5.6 8.5.10,8.5.21
    Thu, 12 Nov Ch. 8.5 8.5.19,8.5.22,8.5.23,8.5.24
    Tue, 17 Nov B.1 B.1.6, B.1.9-B.1.16,B.1.20
    Thu, 19 Nov B.2 B.2.7-B.2.12
    Thu, 24 Nov B.3 all items which are not done in class
    Tue, 1 Dec B.3 all items which are not done in class 8.5.8, 8.5.9
    Thu, 3 Dec problem session
    Tue, 8 Dec An alternative to B
    Thu, 10 Dec problem session/review for the final exam