Math 290-24          Mathematical Reasoning     Fall 2008
Instructor	Office	Phone	Hours
Jimmie Lee Johnson	A. A. Robin Campus Schaumburg, Illinois Room 153	(312) 341-3552 Voice Mail	M 5:00-6:30pm and by appointment.
M 6:30-9:00pm SCH 353
	E-mail:  jjohnson@roosevelt.edu Web Page:  http://faculty.roosevelt.edu/jjohnson/

Text: A Transition to Advanced Mathematics, by Douglas Smith, Maurice Eggen, & Richard St. Andre, Thomson/Brooks Cole, 2006 ISBN 0-534-39900-2.

Prerequisite: Grades of C or better in Math 232 Calculus II or concurrently.

Class will consist of oral reports, quizzes, examples, theorem proving and the answering of questions. Prior to each class, you must do the assigned reading or you will be lost; make notes of topics you feel need elaboration in class. For each class, be prepared to give a short explanation of a definition or proof of a theorem orally, at the chalkboard. You are responsible for all assigned reading even if it is not discussed in class.  Class will usually include
     1. a short quiz each week;
     2. now and then, a short oral presentation of current material by selected students;
     3. discussion of new material via examples and the proof of new theorems.

Quizzes will be given each week beginning September 15th, except for the weeks of the exams. The quizzes will be closed book, and will count for 15% of your grade. The two lowest quiz grades will be dropped. No make-ups; a missed quiz will count as one of the dropped grades.

Homework will be collected, discussed, graded and returned; Homework, along with oral presentation scores, will count for 15% of your grade. Late homework may be downgraded, if it is later than a week, but it is still worth more than no credit at all. I recommend the use of the software Maple to help with examples involving much of the homework.

Exams will be given on October 20th and November 17th These will be closed book . The average of the exams will count for 30% of your grade. No make-ups except for excused absences with advance notice. If you miss an exam, your score on the next exam will be used.

Final Examination will be given on Monday, December 15th, closed book and comprehensive. It will normally count for 40% of your grade.

Grades: Regulations covering grades (especially I and W) are on pages 254-256 of the 2006-2008 Undergraduate Catalog or on pages 203-205of the 2005-2007 Graduate Catalog. Incompletes will not be given, except to a student who has done passing work up to the Final Examination (including most of the homework) but misses the final exam because of an excused absence with advanced notice. The last day to drop a class (with a grade of "W") is Tuesday, November 4th, and the drop form must be submitted to the Registrar's Office. Anyone registered after that must be graded solely on academic performance.

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Objectives: The student is expected to practice both oral and written proving of elementary to difficult theorems in a variety of areas of mathematics. To this end, the completion of a variety of homework problems and oral presentations are expected of each student. For assessment purposes, copies of some graded homework assignments and exams of each student will be placed in a file in the school office. Further review of these materials for assessment purposes will not affect the student's standing.

Syllabus

Date	Sections	Topics -  changeable
September 8	1.1 1.2 1.3	Propositions and Connectives Conditionals and Biconditionals Quantifiers
September 15	1.4 1.5 1.6 1.7	Basic Proof Methods I Basic Proof Methods II Proofs Involving Quantifiers Additional Examples of Proofs
September 22	2.1 2.2 2.3	Basic Concepts of Set Theory Set Operations Extended Set Operations & Indexed Families of Sets
September 29	2.4 2.5 2.6	Induction Equivalent Forms of Induction Principles of Counting
October 6	3.1 3.2 3.3	Cartesian Products and Relations Equivalence Relations Partitions
October 13	3.4 3.5	Ordering Relations Graphs Review
October 20	Exam #1	Chapters 1, 2, 3 -- Lecture Afterward.
October 27	4.1 4.2 4.3	Functions as Relations Constructions of Function Function that are Onto; One-to-One Functions
November 3	4.4 4.5 5.1	Images of Sets Sequences Equivalent Sets; Finite Sets
November 10	5.2 5.3	Infinite Sets Countable Sets Review
November 17	Exam #2	Chapters 3, 4, 5 -- Lecture Afterward
November 24	7.1 7.2 7.3	Ordered Field Properties of the Real Numbers The Heine-Borel Theorem The Bolzano-Weierstrass Theorem
December 1	7.3 7.4 7.5	The Bolzano-Weierstrass Theorem The Bounded Monotone Sequence Theorem Equivalents of Completeness
December 8	6.1 6.2	Algebraic Structures Groups Review
December 15	Final	Comprehensive.

This page is at http://faculty.roosevelt.edu/jjohnson/Fall2008/M290F08.htm and was last revised May 30, 2008.