Math 8 -
Transitions to
Higher Mathematics - Winter 2007
Instructor: Alex Dugas my
homepage
Office: 6510 South Hall
Office Hours: M 1-2, Th 1-3
Prerequisites: Math 3B (with a grade of C or better).
Text: Larry Gerstein. Introduction
to Mathematical Structures and Proofs. Springer-Verlag 1996.
Lecture: T Th
Section: You must sign up for and attend a discussion section as
well.
The section times and locations for this course are as follows:
The GSI for this course is Chad Wiley. His office hours, in SH
6431N,
are:
Announcements:
Course Timetable (subject to change) |
||||
Date |
Topics |
Reading |
Homework |
Due Date |
Tu 1/9 |
Propositions. Logical Connectives: |
Ch. 1.1-1.2 |
Ch. 1.3: Ex. 1, 2, 3, 4, 6, 8, 18 |
1/17 |
Th 1/11 |
More Truth Tables. Conditional Statements and Implications. |
Ch. 1.3 |
||
Tu 1/16 |
Biconditionals.
Converse and Contrapositive of
Implications. |
|
|
|
Th 1/18 |
Logical Equivalence |
Ch. 1.5 |
||
Tu 1/23 |
Functional Propositions. Sets. Russell's Paradox. Axiom of Separation |
Ch. 2.1-2.2 |
Ch. 2.1: Ex. 2, 3b,d, 5, 7
|
|
Th 1/25 |
Universal and Existential Quantifiers |
Ch. 2.3 |
||
Tu 1/30 |
Set Inclusion and Subsets. Unions, Intersections, Complements, Set Difference. Venn Diagrams. |
Ch. 2.4-2.5 |
Ch. 2.4: Ex. 1, 7, 9 |
2/5 |
Th 2/1 |
Power Sets. Indexed Sets. |
Ch. 2.6-2.7 |
Ch. 2.6: Ex. 2a,d, 3, 5 |
|
Tu 2/6 |
Cartesian Products. |
Ch. 2.8 |
|
|
Th 2/8 |
Midterm Exam |
Ch. 1.1 - 1.5, |
|
|
Tu 2/13 |
Relations. Equivalence Relations. Partitions. Partial Orders. |
Ch. 2.9 |
Ch. 2.9: Ex. 4, 6, 10, 20 |
|
Th 2/15 |
Congruence Modulo n. Partial Orders. Induction. |
|
|
|
Tu 2/20 |
Strong Induction. Binomial Coefficients |
|
|
|
Th 2/22 |
Binomial Coefficients. Pascal's Triangle. Binomial Theorem. |
Ch. 5.8 |
Ch. 5.8: Ex. 2, 5, 7, 9, 10 |
|
Tu 2/27 |
Functions. Domain, Image/Range, Surjections. Sets of Functions. |
Ch. 3.1 |
Ch. 3.1: Ex. 1, 6a,b,c,g, 11a,b,e,f |
|
Th 3/1 |
Injections. Bijections. |
Ch. 3.2 |
Ch. 3.2: Ex. 2, 4, 6, 9 |
|
Tu 3/6 |
Composition of Functions. Inverse Functions. |
Ch. 3.3 |
Ch. 3.3: Ex. 2, 3, 4, 7, 8, 9 |
|
Th 3/8 |
Cardinality. Counting Principles. |
Ch. 4.1 |
Ch. 4.1: Ex. 3, 4, 5 |
|
Tu 3/13 |
|
Ch. |
|
|
Th 3/15 |
|
Ch. |
|
|
Th 3/22 |
Final Exam - 12:00 - 3:00 pm |
|
|
|
Course Content: The aim of this course is to familiarize students
with some
of the fundamental tools of mathematics, including sets, functions and
proof, and
how they are written. We will cover most of Chapters 1-3 and
parts of
Chapters 4 and 6 in the text.
Section/Classwork: Attendance
and
participation in a discussion section is mandatory for this
course. In
section, your T.A. will answer questions, review the homework, and
cover
additional examples. But, more importantly, you will work on
problems,
often in small groups. Your work will occasionally be
graded and
contribute to your grade for the course.
Homework: Homework exercises will be
assigned
in lecture and listed in the table above. All homework problems
assigned
in a given week are due on the following Monday in section (or
Wednesday, if
Monday is a holiday). You may work together on homework problems;
however, you must write up your answers individually. You must
show all
your work in order to recieve full
credit. Late
homeworks will not be accepted.
However,
your lowest homework score will be automatically dropped.
Exams: There will be one in-class midterm exam on Thursday
February
8, 11:00 - 12:15. Please arrive promptly. The final
exam will
be Thursday March 22, 12:00 - 3:00 pm. The problems on
the exams
will be similar to ones from classwork and
homeworks. No make-up exams
will be given,
except in extaordinary
circumstances. If you
have a serious conflict with any of these exams or miss one for any
reason, it
is your responsibility to notify me immediately so that other
arrangements may
be made.
Grades: Grades will be computed from your scores on classwork, homeworks
and exams as
follows: Classwork/Section = 10%, Homework
= 25%,
Midterm = 25%, Final = 40%. No letter grades will be assigned
until the
end of the semester, and the exact grading scale will depend on the
difficulty
of the exams. However, a 90% or
above will
guarantee you at least an A, an 80% will be at least a B, and 70% will
be at
least a C.