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**Transition to Advanced
Mathematics**

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Office: Boyd
325

Phone: 770-838-2579

Email: agiovann@westga.edu

Homepage: http://www.westga.edu/~agiovann/

Office Hours: Monday-Thursday 10 a.m. to 11a.m., Monday,
Wednesday, and Thursday 1 p.m. to 2 p.m., Monday and Wednesday 4 p.m. to 5:30
p.m., or by appointment.

Text: A
Transition to Higher Mathematics**,** 5^{th}
edition, by Eggen/St.Andre

Learning
Objectives:

- The student will
demonstrate an understanding of basic symbolic logic by translating
English sentences to formal logical expressions and translating formal
logical expressions to equivalent English sentences (L2).
- The student will be
able to state the basic definitions and use the notation of naïve set
theory (L2).
- The student will be
able to state the basic definitions, properties, and use the notation of
functions, including terms like injection, surjection, and bijection (L2, L5).
- The student will know
and use the definition of cardinality of sets and will be able to
determine the cardinality of given sets, when two sets have the same
cardinality, and the relationship of cardinality and bijections of sets (L2, L5).
- The student will be
able to distinguish between finite sets and infinite sets (L2, L5).
- The student will use
mathematical arguments, including direct proofs, proofs by contradiction,
proofs by induction, and proofs by contra-positive to prove facts about
sets, functions and basic algebraic objects (L2).
- The student will
demonstrate that he/she can comprehend symbolically written mathematics by
explaining in his/her own words definitions, statements of theorems, and
other mathematically written sentences (L2, L4).
- The student will be
able to write facts, arguments, and/or questions about mathematics using
correct grammatical style for both the English and mathematical text (L2, L4).

Assessment:

10-12
Short
in-class Responses (WTL exercises)

These will be one to five
sentences written responses to questions raised in the lecture. Each part will
be assigned from 0-4 points of these 0-2 will be given for content and 0-2 for
style.

3
75-minute
tests during class periods.

1
Comprehensive
Final

3-4
Short
oral presentations and write-up. Each will be graded on a 5-point scale. The presentation will be 0-3 points and
judged on coherence and clarity of presentation. (An extra point can be gained by using technology in the
presentation.) The write-up (a WTL
exercise) will be 0-2 points and graded on clarity of style, grammar, and
spelling. The write-up is due two class
periods after the presentation. The max
score for the write up will be reduced by one point per class period if handed
in late. References must be included.
The reference style should be the AMS style.
Examples of this style can be found in **The American Math
Monthly. **

1
Paper
5-8 pages in length. (Illustrations and
graphs not to be included in the page count.) (WTC exercise) The paper should
be typed or printed. The text should be
double spaced and using a 12pt font.
Topics may be selected from people, problems, schools or controversies
in mathematics and must have the instructors consent. The bibliography must include at least 2 books, 2 journal
articles and 2 Web addresses references.
The style of the bibliography should be the AMS style. The outline and rough draft will be read and
handed back with helpful suggestions only if handed in by the dates given
below.

Your
course grade is based on these 7 parts as follows:

Test 1 15%

Test 2 15%

Test 3 15%

Final 15%

Presentations and write-ups 15%

Paper 20%

Letter grade:
A_{}90>B_{}80>C_{}70>D_{}60>F

Dates:

October
3 Outline of paper due.

October
10 Last day to withdraw with a W

October
24 Rough draft of paper due.

October
24 Test 2

November
26 Test 3

December
3 Final draft of paper due (Last
Class)

December
10 Final Exam 11 a.m. to 1 p.m. in
Boyd 206

*
NOTE: A “W” designation after a section number signifies that the course is a
Writing Across the Curriculum (WAC) course. WAC accepts as a guiding principle
the idea that writing is a valuable tool for learning and communication.
Therefore, the writing components of a course so designated are designed to
help you learn the material and communicate what you have learned. Students are
required to take two “W” courses for an undergraduate degree in the College of
Arts and Sciences.