Introduction to analysis (Math 131A), Spring 2024

MacQuarrie Hall 234, MW noon-1:15pm (Sec. 01, code 21491)

Last update of this page: Tue May 07, 9:00pm

Ongoing useful links:

• Class Gradescope page
• How to get started on Gradescope (includes several useful videos)
• The Gradescope mobile app for scanning documents into Gradescope using your smartphone
• Older tips for scanning documents into Gradescope

Announcements:

• The textbook for this class is Elementary Analysis: The Theory of Calculus, by Kenneth Ross. Make sure you get the second edition with the blue and yellow cover. We will be using the textbook immediately, and supplies are limited at the bookstore, so please buy your copy as soon as possible.
• If you'd like to do some review/self-study on methods of proof, you might try looking at my Math 108 course notes or Reading, Writing, and Proving, by Daepp and Gorkin. Since Math 131A is essentially about proving calculus, you may also want to review calculus using your favorite calculus textbook.
• Click here to go to our Canvas page (not often used).
• We will hold weekly problem sessions every Friday, noon-2pm, by Zoom.
• If you're interested in typesetting math, the system I use to make my handouts is called LaTeX, and it can be downloaded for free (in Windows format) at http://www.miktex.org. If you own a Mac (system OS X) or a Linux computer, you already own a copy of this program, as it's been a standard Unix program for about 20 years. And for our purposes, the key point is that under any system, LaTeX can produce pdf output that is ideal for online homework submission.
  LaTeX is well worth learning, if you have some free time; it's used for manuals and technical reports throughout nerd-dom. For self-study, I highly recommend the LaTeX book by Leslie Lamport, which you can purchase here.

FUA (Frequently Used Acronyms):

Administrative handouts:

Course greensheet.

Course notes and other resources:

Course mechanics: Homework in Math 131A, Check-ins, Workflow.

Course content:

• Writing proofs
• Summary of main theoretical points of Math 131A
• (Sect. 3) Axioms for the real numbers
• Model outline for PS01
• (Sect. 7) The Wolfram Alpha sequence grapher widget
• (Sect. 9) Fractionology and asymptotics
• (Sect. 9) Using the Limit Laws in logical order
• (Sect. 14) More about tests for convergence/divergence of series and rearrangements of series
• Notes on the Riemann integral (summary in slides)
• (Sects. 23-26) Pointwise vs. uniform convengence

The official web page for our textbook, which includes two helpful lists of errata.

Topics for exams:

Exam 1, Exam 2, Exam 3, Final exam.

Sample exams:

Exam 1, Exam 2, Exam 3, Final exam.

Problem sets:

HW	Outline due	Definitions from sections	Due date	Last revision due	Problems to be done but not turned in	Problems to be turned in
PS00	n/a	n/a	Wed Jan 31	n/a	n/a	See handout.
PS01	Wed Jan 31	Sec 3 (starting with Defn 3.3), 4	Mon Feb 05	Fri Mar 01	3.1, 3.3, 3.5, 3.7, 4.1, 4.3, 4.5, 4.7, 4.9, 4.11, 4.13, 4.15.	See handout (LaTeX source).
PS02	Wed Feb 07	Sec 5, 7	Mon Feb 12	Fri Apr 12	5.1, 5.3, 5.5, 5.7, 7.1, 7.3, 7.5.	See handout (LaTeX source).
PS03	Wed Feb 14	Sec 8, 9	Mon Feb 19	Fri Apr 12	8.1, 8.3, 8.5, 8.7, 8.9, 9.1, 9.3, 9.5, 9.7, 9.9, 9.11, 9.13, 9.15, 9.17.	See handout (LaTeX source).
PS04	Thu Feb 29	Sec 10, 11	Tue Mar 05	Fri Apr 12	10.1, 10.3, 10.5, 10.7, 10.9, 10.11, 11.1, 11.3, 11.5, 11.7, 11.9, 11.11; also see handout.	See handout (LaTeX source).
PS05	Wed Mar 06	Sec 12, 14	Mon Mar 11	Fri May 03	12.1, 12.3, 12.5, 12.7, 12.9, 12.11, 12.13; 14.1, 14.3, 14.5, 14.7, 14.9, 14.11, 14.13.	See handout, corrected Tue Mar 05 (LaTeX source).
PS06	Thu Mar 14	Sec 15, 17	Tue Mar 19	Fri May 03	15.1, 15.3, 15.5, 15.7; 17.1, 17.3, 17.5, 17.7, 17.9, 17.11, 17.13, 17.15.	See handout (LaTeX source).
PS07	Tue Mar 26	Sec 18, 19, 20	Fri Mar 29	Fri May 03	18.1, 18.3, 18.5, 18.7, 18.9, 18.11; 19.1, 19.3; 20.1, 20.3, 20.5, 20.7, 20.9, 20.11.	See handout (LaTeX source).
PS08	Wed Apr 10	Sec 28	Mon Apr 15	TBA	20.13, 20.15, 20.17, 20.19; 28.1, 28.3, 28.5, 28.7, 28.9, 28.11, 28.13, 28.15.	See handout (LaTeX source).
PS09	Thu Apr 18	Sec 29, notes on the Riemann integral	Tue Apr 23	TBA	29.1, 29.3, 29.5, 29.7, 29.9, 29.11, 29.13, 29.15, 29.17, 32.1, 32.3, 32.5, 32.7, 33.1, 33.3, 33.7, 33.9, 33.11, 33.13.	See handout (LaTeX source).
PS10	Fri May 03	Sec 23, 24	Tue May 07	TBA	23.1, 23.3, 23.5, 23.7, 23.9, 24.1, 24.3, 24.5, 24.7, 24.9, 24.11, 24.13, 24.15, 24.17.	See handout (LaTeX source).
PS11	Fri May 10	Sec 25, 26	Tue May 14	TBA	25.1, 25.3, 25.5, 25.7, 25.9, 25.11, 25.13, 25.15, 26.1, 26.3, 26.5, 26.7.	See handout (LaTeX source).

Reading assigned in course:

In course notes: Fractionology and asymptotics, More about tests for convergence/divergence of series, Rearrangements of series, Uniform vs. pointwise convengence.

Optional review reading: Ross Sections 1-2; Proof handout: Sections 1-6, 7, 9, 11, 13-14.

Other useful links:

• If you're interested in typesetting math, the system I use to make my handouts is called LaTeX. If you have a Windows PC, you can download LaTeX for free at http://www.miktex.org; you will also need a good text editor, like the shareware program WinEdt. PCTeX also makes a good commercial version; student prices are $150 for the "Publisher" version, which I recommend if you have the money, $50 for the "Writer" version, which I recommend if you don't. If you own a Mac, you can download a complete system called TeXShop for free. If you own a Linux computer, you already own a copy of this program, as it's been a standard Unix program for about 20 years.

  LaTeX is well worth learning, if you have some free time; it's used for manuals and technical reports throughout nerd-dom. For self-study, I highly recommend Learning LaTeX (Griffiths and Higham) for beginners, and the LaTeX book by Leslie Lamport as a reference.

• Free downloads: Adobe Acrobat (for reading .pdf files)

• Instructor: Tim Hsu.
• Required text: Elementary Analysis: The Theory of Calculus, by Kenneth Ross (2nd edition, 2013, blue and yellow cover).
• Suggested texts: Writing Proofs, Hsu (download here); any calculus textbook that you like.
• Homework: Outline and final version due once each week, except in exam weeks. For details, see the handout on homework in Math 131A.
• Exams: Three in-class 75-minute exams, plus 2 hour, 15 min final exam (Fri May 17, 9:45am-noon).
• Grading: Final course grades consist of:
  

  Homework:	20%
  Exam 1:	14%
  Exams 2 & 3:	18% each
  Final:	30%