## Math 95: Transition to Upper Division Mathematics Summer Session C, 2017, Course Syllabus

INSTRUCTOR: Michael Andrews Office: MS 6322 Email: mjandr@math.ucla.edu Austin Christian Office: MS 3969 email: archristian@math.ucla.edu As the name of this class suggests, its purpose is to help students transition from lower division classes in mathematics to upper division classes in mathematics. This is not an easy transition. Sadly, in lower division classes, mathematics is sometimes taught as a bunch of formulae and procedures to memorize. I usually refer to this as "plug-and-chug." This approach to learning/teaching mathematics does not inspire: - pattern spotting; - deep thinking and careful reasoning in order to justify the truth of an observed pattern. These two bullet points are what all of mathematics has in common. The pattern spotting requires imagination; the proof of such patterns requires careful adherence to the "rules" of mathematics. Upper division mathematics focuses on both bullet points. The first may sound more interesting to you, but, because of the abstract nature of mathematics, at a certain point, it becomes impossible to do mathematics without developing the second skill, and this is what students find most difficult. This class will focus on the second bullet point extensively. The patterns that we discuss will, on the whole, not be complicated, but clearly expressing our arguments concerning them will require a lot of practice. You should see this class as a fresh start. Although, I will expect some basic lower division math skills, I will not expect you to recall anything about 3-dimensional integrals, differential equations, or linear algebra. Much of the mathematics you have already seen was not taught with the intension of being completely rigorous or completely understandable from the ground up. In this class, we will prove everything rigorously, and you should be striving for a complete understanding of all the material. If you wish to see what sort of material we will cover, look at the contents page of the lecture notes (the actual notes are yet to be filled in). Another goal of this class is to prepare you for Math 131A. You will see some overlap with the material of that class. My lecture notes for 131A can be found here. BOELTER 2760; Monday, Tuesday, Wednesday; 9:00am-10:50am. BOELTER 2760; Thursday 9:00am-10:50am. Monday 11am-1pm (Austin), Tuesday 11am-1pm (Austin), Tuesday 2pm-4pm (Michael), Thursday 11am-1pm (Austin), Friday 10am-1pm (Michael; joint with 131A) You will receive assignments in weeks 1,2,3,4 to prepare you for the quiz the following week. Wednesday 10:10am-10:50am in weeks 2,3,4,5. Wednesday 13th September (the final day of class) 9:00am-10:50am. You will receive the better of scheme 1 and 2. Scheme 1: quizzes worth 18% each; final worth 46%. Scheme 2: one quiz dropped, the others worth 18% each, final 64%. Steven R. Lay, Analysis: With an Introduction to Proof. Pearson. Fifth Edition. However, my notes should serve you better.