Math 104: Introduction to Real Analysis (2021 Fall)
Instructor: Peng Zhou
Office: Evans 931
Office Hour: Monday 12:10-1pm, Tuesday 11:10-12. Friday 10-11pm
Lecture: MWF, 11:10am - 12:00. Etcheverry 3107.
GSI: James Dix. Mondays 9am-6pm, Wednesday 12-2pm in Evans 1049.
20% homework; 2 midterms 20% + 20%; and final 40%. If you didn't do well in one of the midterm, you have the option to drop it, and final will have a 60% weight. The lowest homework grades will be dropped.
Midterm date: 9/22 (Wed), 11/3 (Wed). There will be no make-up midterms.
Homework will be submitted via gradescope. Entry Code:YVZRDZ
part 1: number system, sequence and limit, series.
part 2: metric space and topology. continuity.
part 3: differentiation and integration.
Aug 25: introduction. counter-examples. Tao, Ch 1.
Aug 27: Peano Axioms for natural numbers. (Tao Ch2). Inadequacy of $\Q$. Least upper bound (Rudin Ch 1, section 1)
Reading homework; Tao Ch 1 and 2. Rudin Ch 1.
Aug 30: More about sup. Definition of field.
Sep 1: Cauchy sequence of rational numbers.(Tao 5.2)
Sep 3: Equivalent Cauchy sequences of rational numbers as real numbers. Operation and properties of real numbers. (Tao 5.3)
Tao Ch 6. Ross Ch 2.1 - 2.7.
Sep 13: Sequences in $\R$. Convergent implies Cauchy. Arithmetic operation commute with limit. Bounded monotone sequences are convergent. limsup.
Sep 15: $\pm \infty$. Tao 6.4. Cauchy sequences are convergent.
Sep 17: Finish Cauchy sequence is convergent. Limit points and subsequence.
Due next Tuesday 6pm
Sep 22 (Midterm 1)