MATH U2000: Introduction to Higher Math
Fall 2017
The most up-to-date information on this course can be found on the Courseworks page for this course.
Time and place: MW 8:40--9:55am Location: LLL103 Diana Center
Lecturer: Walter Neumann (x45074, 616 Mathematics,
neumann@math.columbia.edu,
www.math.columbia.edu/~neumann);
office hours MW 1:30-2:30 or by appointment.
This course is designed to introduce you to the language and precise thinking of higher mathematics. In particular, it is designed to be a preparation for the "proof based" mathematics you will meet in more advanced courses such as our Modern Algebra and Modern Analysis sequences. It is particularly useful for student intending majoring in mathematics but wish additional training.
Recommended Text: Transition to Higher Mathematics by Bob A. Dumas
John E. McCarthy
If you google you might find it online.
Tentative syllabus:
Sep 6,11,13: Ch 1 (some logic, sets and functions)
Sep 18,20: Ch 2 (relations, modular arithmetic)
Sep 25,27: Finish Ch 2, Ch 3 (logic and proofs, through 3.3)
Oct 2: Review Oct 4: MIDTERM I
Oct 9, 11: finish Ch 3 (quantifiers, proof strategies).
Oct 16, 18: Ch 4.1, 4.2 (proofs by induction)
Oct 23, 25: Ch 5.1, 5.2 (sequences, limits and continuity)
Oct 30, Nov 1: finish discussion of Ch 5 and start Ch 6
Nov 6: Academic Holiday
Nov 8: Review Nov 13: MIDTERM II
Nov 15, 20: Ch 6 (cardinality)
Nov 27, 29: Ch 7 (divisibility)
Dec 4, 6: Ch 8 (Real numbers)
Dec 10 Review
Homework: There will be weekly problem sets, due in the homework box on the 4th floor Mathematics by 1pm on Wednesdays. Although only a portion of the homework will be graded, you should attempt every homework problem and eventually understand how to do every problem correctly. Collaboration and discussion with classmates is encouraged, but you must write up assignments individually.
Exams: There will be two in-class midterm exams and a final. Schedule:
Grading: The final course grade will be determined by:
Homework: 25%
Midterm exams each: 25%,
Final exam: 25%.
Help: My office hours are MW 1:30-2:30 or by appointment. Help is also available without appointment in the Mathematics help room (406 Mathematics).