• Meeting Time & Place:
  • Lecture: ST 107, Tuesday, Thursday, 4:00-5:15 PM
• Instructor: Dr. George D. Tintera
• Office: Center for Instruction 303 (CI 303)
• Office Hours: M: 2:30 to 4:00 PM; TR 1:00 to 4:00 PM
  Appointments also available. Office hours subject to meetings related to other duties on campus. They may change during the semester.
• Phone: (361) 825-6028, FAX: (361) 825-2795
• Internet: tintera@falcon.tamucc.edu
• Class Website: http://www.tamucc.edu/~tintera/f03/3313

II. COURSE DESCRIPTION

This course assists students in the transition from lower-level courses such as calculus to higher-level courses such as advanced calculus and modern algebra. While lower-level mathematics courses emphasize skills and techniques needed for courses outside mathematics, higher-level mathematics courses require students to understand and write proofs and to think more abstractly. This course introduces students to fundamental ideas in logic and set theory needed for courses in higher mathematics and for secondary school and collegiate teaching. Techniques of proof, such as proof by contradiction and proof by induction, are used in various settings, such as analytic geometry and coordinate systems. The proper use of quantifiers, multiply quantified statements, properties of functions and relations on sets, modular arithmetic and equivalence relations, and partial orderings are emphasized. Examples used in this course will be taken from number theory, combinatorics, graph theory, modern algebra, and advanced calculus.
The following topics will be covered:

• Set Theory, Logic and Propositional Calculus
• Logic and Predicate Calculus (Quantifiers)
• Applications to Proofs in Set Theory
• Methods of Proof (Mathematical Induction, Indirect Proofs, Epsilon-Delta Proofs)
• Relations (Equivalence Relations, Equivalence Classes, Partial Orderings)
• Functions and Mappings (Injective, Surjective, Bijective, Image, Inverse Image)
• Cardinality of Sets
• Axioms of Real and Complex Number Systems
• Geometry of Complex Arithmetic
• Introduction to Advanced Calculus

Please note that this class is a prerequisite for MATH 4301, Advanced Calculus, and MATH 4306, Modern Algebra. This prerequisite will be enforced. If you do not get a grade of C or better in this course, you will need to repeat it before being permitted to take 4301 or 4306.

III. PREREQUISITES FOR THE COURSE

MATH 2414 Calculus II and MATH 2305, Discrete Math.

IV. TEXT AND OTHER SUPPLIES REQUIRED

A Transition to Advanced Mathematics, by Smith, Eggen and St. Andre, Brooks/Cole, 5th ed. is required. The book Mathematics for High School Teachers: An Advanced Perpective, by Usiskin, Peressini, Marchisotto and Stanley, Prentice Hall is recommended as a reference for future (and current) teachers.

V. COURSE OBJECTIVES

Students completing this course will learn to do the following:

• Understand the structure and properties of the real and complex number systems
• Read and understand arguments involving set theory and logic with minimal assistance from the instructor
• Generalize mathematical observations of special cases
• Write proofs of basic results in advanced calculus and set theory which include multiply quantified statements
• Present mathematically precise arguments to peers, beginning college students, and secondary school students
• Develop reasoning skills needed in higher mathematics course work and mathematics teaching

VI. INSTRUCTIONAL METHODS AND ACTIVITIES

The class uses a discussion format with room for presentations by students as well as the instructor. Students are expected to read the text before class as directed and be prepared to participate in the class. This may include presenting written materials at the board with or without notes.

VIII. EVALUATION AND GRADE ASSIGNMENT

Grades:

In-class presentations, answers to questions and pop-quizzes 20%
Homework: 20%
Midterm: 20%
Project: 10%
Final Exam: 30%

After a semester average is computed from the above, letter grades will be assigned according to the customary scale:90-100 = A; 80-89 = B; 70-79 = C; 60-69 = D; under 60 = F. In borderline cases, I give extra weight to the final exam and midterm, in that order.

Group work: In general, in-class and at-home work on exercises may be done collectively. When turning such work in, it is expected that you acknowledge all assistance you received on an assignment. Misrepresenting someone else's work as your own may be grounds for a charge of Academic Dishonesty.

Homework: A page detailing homework and due dates will be posted. It will be returned as asoon as possible.

A project will be assigned to be completed during the last third of the course. The purpose of that project is for students to apply their understanding of the course so far to various mathematical topics.

VIII. TENTATIVE COURSE SCHEDULE (Attached.)

IX. CLASS POLICIES

Attendance: I take attendance daily. Absences are unexcused until they are excused in writing. Write as soon as reasonably possible (email is OK) asking for an absence to be excused.

Late Homework: Late homework is not accepted. Homework that is completed to the best of your ability is expected. Homework that is not done well enough will be returned and expected back within a week. The last day homework can be turned in is the last day of class in the semester.

Help: The tutors you may have used in the past may not be able to help you with this course. The better sources of help are fellow classmates and the instructor. If you intend to seek the tutelage of someone else, please let the instructor know.

ADA: The Mathematics Program complies with the Americans with Disabilities Act in making reasonable accommodations for qualified students with disabilities.  If you need disability accommodations in this class, please see me as soon as possible.  Please have your accommodation letter from TAMU-CC Services for Students with Disabilities Office with you when you come see me.  If you suspect that you may have a disability (physical impairment, learning disability, psychiatric disability, etc.), please contact the Services for Students with Disabilities Office (located in Driftwood 101) at 825-5816.  It is important that you contact them in a timely fashion as it may take several days to review requests and prepare accommodations.