Course:
MATH 199

Section 45: MWF 11:30-12:20 p.m., Eckhart 312

Section 55: MWF 12:30-1:20 p.m., Eckhart 312

Instructor: Dr. E. Strawbridge

Email: emstrawb "at" math.uchicago.edu

Course Web Page: www.math.uchicago.edu/~emstrawb/math_199.html

Office Hours: MW 9:00-10:00 a.m., W 1:30-2:30 p. m., R 10:00-10:30am E326

Course Description: A course description and necessary prerequisites can be found in your course catalog or at the following link to the Math Department Webpages.

Course Content: This course covers the fundamentals of theoretical mathematics and prepares students for upper-level mathematics courses beginning with Math 20300. We begin the syllabus with set theory and functions, including DeMorgan's Laws and the notions of injectivity and surjectivity. Next we move on to the axioms for fields and for ordered fields, and we derive many consequences (e.g. uniqueness of inverses). Taking the rational numbers as given, we then construct the real numbers via equivalence classes of Cauchy sequences and prove that they form an ordered field satisfying the least upper bound axiom. From that point on, the course follows two major topics in natural progressions: the topology of the real line up through the Nested Intervals Theorem, and linear algebra from vector spaces and bases through linear maps and matrices.

Prerequisites: MATH 15300.

Required Text: Tools of the Trade: Introduction to Advanced Mathematics. by Paul J. Sally, Jr. (ISBN # 978-0-8218-4634-6),

Participation and Attendance: Attendance will not be taken but homeworks will be collected at the beginning of class. Homeworks not turned in at this time will be given a zero. Lecture and discussion participation and attendance are highly recommended.

Grading: The course grade is based on the top 9 of 10 total homeworks, the top 9 of 10 quizzes, 2 Midterms, and a Final.

Quizzes 5%

Midterm 1 25%

Midterm 2 25%

Final 25%

Homework 20%

The midterms will not be cumulative in the strict sense of the word. However, it will be necessary to know previous material. The dates and times of the Midterms and the Final are listed in the Syllabus. Midterm 1 will cover Chapter 1, Midterm 2 will cover Chapter 3. The Final will be cumulative and will cover Chapters 1-3. The date, time, and place of the Final is fixed.

**Final Exam Policy:**
It is the policy of the Department of Mathematics that the following rules apply to final exams
in all undergraduate mathematics courses:

The final exam must occur at the time and place designated on the College Final Exam Schedule. In particular, no final examinations may be given during the tenth week of the quarter, except in the case of graduating seniors. You must take your exam at the date and time for your section.
Any student who wishes to depart from the scheduled final exam time for the course must receive permission from Paul Sally (office is Ry 350, phone is 2-7388, email is sally "at " math.uchicago.edu). Instructors are not permitted to excuse students from the scheduled time of the final exam except in the case of an Incomplete.

Homework: Homework will be assigned weekly on Friday and will be due at the beginning of class on the following Friday (or Wed. if the Friday is a holiday or reading day). There will be a total of 10 homeworks and the lowest score will be dropped. Homework and must be turned in at the beginning of class. The list of problems will be given in class in Fridays and can also be found here.

Quizzes: Quizzes will be given at the beginning of class on each Wednesday. There will be a total of 10 quizzes and the lowest score will be dropped. Quiz solutions are available here.

Exam Policies: All exams are closed book and close notes. No calculators or electronic devices are allowed. Cell phones may not be used as calculators or clocks.

Policies for Missed Exams or Quizzes: It is the student's responsibility to notify the instructor prior to the exam/quiz date if there is a conflict. Midterms may be given early so long as the student makes the proper arrangements with the instructor. Any rescheduling of an exam/quiz requires proof of reason. There will be NO late exams/quizzes allowed. If a student misses a midterm for unforeseeable, emergency reasons and the student can provide proof of the emergency, then arrangements may be made so that the student does not receive a zero for that exam/quiz. The Final cannot be missed.

Policies for Late Homework: No late homeworks are accepted. Late or missing homeworks will be given a zero.

Electronic Devices: Please make certain that all cell phones and pagers are TURNED OFF before lecture begins. Cell phones and pagers are disruptive to the whole class.

Obligatory Statement About Academic Fraud: All work in this course must be of your own original composition. Students are welcome to work in groups on homework but each student must submit his or her own homework. Unethical behavior during exams, such as unauthorized crib notes, looking at a neighbors exam, or communication during an exam (verbal, written, electronic, or otherwise) will not be tolerated.

Section 45: MWF 11:30-12:20 p.m., Eckhart 312

Section 55: MWF 12:30-1:20 p.m., Eckhart 312

Instructor: Dr. E. Strawbridge

Email: emstrawb "at" math.uchicago.edu

Course Web Page: www.math.uchicago.edu/~emstrawb/math_199.html

Office Hours: MW 9:00-10:00 a.m., W 1:30-2:30 p. m., R 10:00-10:30am E326

Course Description: A course description and necessary prerequisites can be found in your course catalog or at the following link to the Math Department Webpages.

Course Content: This course covers the fundamentals of theoretical mathematics and prepares students for upper-level mathematics courses beginning with Math 20300. We begin the syllabus with set theory and functions, including DeMorgan's Laws and the notions of injectivity and surjectivity. Next we move on to the axioms for fields and for ordered fields, and we derive many consequences (e.g. uniqueness of inverses). Taking the rational numbers as given, we then construct the real numbers via equivalence classes of Cauchy sequences and prove that they form an ordered field satisfying the least upper bound axiom. From that point on, the course follows two major topics in natural progressions: the topology of the real line up through the Nested Intervals Theorem, and linear algebra from vector spaces and bases through linear maps and matrices.

Prerequisites: MATH 15300.

Required Text: Tools of the Trade: Introduction to Advanced Mathematics. by Paul J. Sally, Jr. (ISBN # 978-0-8218-4634-6),

Participation and Attendance: Attendance will not be taken but homeworks will be collected at the beginning of class. Homeworks not turned in at this time will be given a zero. Lecture and discussion participation and attendance are highly recommended.

Grading: The course grade is based on the top 9 of 10 total homeworks, the top 9 of 10 quizzes, 2 Midterms, and a Final.

Quizzes 5%

Midterm 1 25%

Midterm 2 25%

Final 25%

Homework 20%

The midterms will not be cumulative in the strict sense of the word. However, it will be necessary to know previous material. The dates and times of the Midterms and the Final are listed in the Syllabus. Midterm 1 will cover Chapter 1, Midterm 2 will cover Chapter 3. The Final will be cumulative and will cover Chapters 1-3. The date, time, and place of the Final is fixed.

Homework: Homework will be assigned weekly on Friday and will be due at the beginning of class on the following Friday (or Wed. if the Friday is a holiday or reading day). There will be a total of 10 homeworks and the lowest score will be dropped. Homework and must be turned in at the beginning of class. The list of problems will be given in class in Fridays and can also be found here.

Quizzes: Quizzes will be given at the beginning of class on each Wednesday. There will be a total of 10 quizzes and the lowest score will be dropped. Quiz solutions are available here.

Exam Policies: All exams are closed book and close notes. No calculators or electronic devices are allowed. Cell phones may not be used as calculators or clocks.

Policies for Missed Exams or Quizzes: It is the student's responsibility to notify the instructor prior to the exam/quiz date if there is a conflict. Midterms may be given early so long as the student makes the proper arrangements with the instructor. Any rescheduling of an exam/quiz requires proof of reason. There will be NO late exams/quizzes allowed. If a student misses a midterm for unforeseeable, emergency reasons and the student can provide proof of the emergency, then arrangements may be made so that the student does not receive a zero for that exam/quiz. The Final cannot be missed.

Policies for Late Homework: No late homeworks are accepted. Late or missing homeworks will be given a zero.

Electronic Devices: Please make certain that all cell phones and pagers are TURNED OFF before lecture begins. Cell phones and pagers are disruptive to the whole class.

Obligatory Statement About Academic Fraud: All work in this course must be of your own original composition. Students are welcome to work in groups on homework but each student must submit his or her own homework. Unethical behavior during exams, such as unauthorized crib notes, looking at a neighbors exam, or communication during an exam (verbal, written, electronic, or otherwise) will not be tolerated.