Syllabus for M 307, Spring 2015
Introduction to Abstract Mathematics
Meeting Time: MWF 8:10 - 9:00
Location: Math 108.
Professor: Jennifer Kacmarcik
Office: Math 107
Office Phone: 243-2083
e-mail: jennifer.kacmarcik@mso.umt.edu
webpage: http://www.math.unt.edu/halfpap
Office Hours: Monday 1:10 – 2:00, Tuesday 10:10 – 11:00, Wednesday 9:10 – 10:00.
Text: Exploring the Infinite: An Introduction to Proofs and Analysis, Jennifer Kacmarcik.
To be made available electronically.
Course Description
This course is designed to help you develop the tools needed in upper-division proofbased courses. This is the course in which you make the transition from a learner of
mathematics to a creator of mathematics.
More specifically, the goals for this course are:
1. Course overarching learning goals:
a. to develop a facility in using the language of mathematics, to learn the
language of mathematics and to gain understanding of mathematical rigor.
b. to learn how to read, construct, and write proofs and recognize when the
reasoning is correct and when it is incorrect.
c. to create and develop the ability to reason mathematically as demonstrated
by the construction of proof strategies, methods and techniques and the
clearness with which a proof is written.
d. to learn to work in the realm of abstract mathematics, correctly applying
definitions, axioms, and theorems.
e. to create and develop students' critical thinking ability and independent
thought.
2. Assessed learning goals:
a. to learn the basics of mathematical logic (propositional and predicate
calculus).
b. to learn how to construct and write direct proofs, contrapositive proofs, proofs
by contradiction, and proofs by mathematical induction.
c. to learn set-notation, and techniques, to prove set-theoretic properties.
d. to learn properties of abstractly defined functions and relations.
e. to gain understanding of injections, surjections and bijections, and their use in
comparing cardinalities of sets.
f. to understand how the various numbers systems (natural numbers, integers,
rational numbers, real numbers, complex numbers) can be introduced
rigorously, and to learn the distinguishing properties of these numbers
systems.
Assessment
Homework: 25%
Exams: 30%
Portfolio: 20%
Final: 25%
Homework: In upper-division courses, the homework assignments serve a different
purpose than homework assignments given in 100- and 200-level courses; in the latter
case, the main purpose of the homework is to give you practice with the basic ideas and
techniques, and the grade is determined mostly through exams. In most upper-division
courses, the “practicing" occurs on your own as you work through suggested exercises
from the text and examples from the lecture. The homework assignments are where you
are asked to bring together ideas and where you are to practice your mathematical
writing skills. Homework is now a very important part of the assessment.
Homework is due each Wednesday. You are encouraged to work together and get all
the help you need.
Exams. There are three midterm exams. Exams serve a different purpose in upperdivision courses because the purpose of the course is no longer to learn to solve certain
problem types quickly and accurately. Exams will tend to focus of definitions, points of
logic, and the more routine types of proofs.
Portfolio. This is the part of the course in which you will really focus on learning to write
mathematics clearly. Every other week, you must select a new problem to add to your
portfolio. Solutions are to be typed using latex. You will submit first a draft of your
portfolio problem. I will comment on, but not grade, the solution at that time. The
portfolio is submitted for grading at two points during the semester. {\it Portfolio
problems are to be entirely your own work; you may ask me questions, but you may not
work with others and may not consult other sources.} View the portfolio as a sort of
take-home exam stretched over time, with a revision process.
Final. The final exam will be comprehensive and given during the regular final exam
period, which is Monday, May 11, 10:10 - 12:10.
Academic Misconduct
All students must practice academic honesty. Academic misconduct is subject to an
academic penalty by the course instructor and/or a disciplinary sanction by the
University. All students need to be familiar with the Student Conduct Code. The Code
is available for review online at
http://www.umt.edu/SA/VPSA/index.cfm/page/1321.\medskip
Students with Disabilities
Students with disabilities may request reasonable modifications by consulting with me.
The University of Montana assures equal access to instruction through collaboration
between students, instructors, and Disability Services for Students (DSS). For more
information, consult http://www.umt.edu/disability. \medskip
Important Dates
Feb. 13 (Fri.): Last day to add/drop via Cyberbear.
Feb. 16 (Mon.): Presidents' Day Holiday.
Feb. 27 (Fri.): Exam 1.
Mar. 13 (Fri.): Portfolio I Due.
Mar. 27 (Fri.): Exam 2.
Mar. 30 - April 3 (Mon. - Fri.): Spring Break.
April 6 (Mon.): Last day to drop without Dean's signature.
May 1 (Fri.): Exam 3.
May 8 (Fri.): Last day of class. Portfolio II due.
May 11 (Mon.): Final Exam, 10:10 - 12:10.