Introduction to analysis (Math 131A), Spring 2018

MacQuarrie Hall 235, MW 10:30-11:45am (Sec. 02, code 26208)

Last update of this page: Mon May 14, 9:45am

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.

• Our weekly sessions will be held every Friday, from 10am-noon, in MacQuarrie Hall 425. Note that the room may be subject to change.

• Homework for this class can be submitted either in person or online. If you want to submit a homework assignment online, please submit it via Canvas, which you probably know how to use better than I do. (If you don't, check out the tutorials here; the only part of Canvas we will use is online assignment submission.) If Canvas doesn't know that you're enrolled in this course, please email me at tim.hsu@sjsu.edu, and I'll make that happen ASAP.

  If you submit homework online, I will very much appreciate it if you can use a document scanner app to produce a single PDF file instead of lots of jpegs (photos). For most phones, either a document scanner app comes with the phone, or you can get one for free or at least cheap. Specifically:

  • If you have an Android phone, click here to see instructions on how to use the Google Drive app as a document scanner.
  • If you have an iPhone, click here to see how to use the Apple Notes app as a document scanner.
  There are also various free and paid apps for doing document scans; check your phone's app store.

  Also, when you name your file(s), please use the following filename convention. (The convention is shown here for a student named Sarah Jane Smith doing PS01 and submitting in pdf format; please substitute your own name, PSxx, and your file format as appropriate.)

  • Outline: PS01-outline-Smith.pdf
  • Complete PS01: PS01-Smith.pdf
  • Revision number 1: PS01-rev1-Smith.pdf (and similarly for further revisions)
  
  If there's more than one Smith in the class, I'll let you know, and you can use something like PS01-Smith-SJ.pdf.

• 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.

• Slides from class on:
  • Axioms for the real numbers

• Maple worksheets used in class: None yet.

FUA (Frequently Used Acronyms):

Administrative handouts:

Course notes:

Course content:

• Overview of Math 131A
• (Sect. 3) Axioms for the real numbers
• (Sect. 9) Fractionology and asymptotics.
• (Sect. 14) More about tests for convergence/divergence of series and Rearrangements of series.
• Hsu Math 131B textbook: 3.3, 4.2, 4.3.
• (Sects. 23-26) Uniform convengence, The five NOs, Still NO for differentiation.

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

Topics for exams:

Sample exams:

Problem sets:

HW	Outline due	Due date	Last revision due	Problems to be done but not turned in	Problems to be turned in
PS01	Wed Jan 31	Mon Feb 05	Wed Feb 21	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	Mon Feb 12	Wed Mar 21	5.1, 5.3, 5.5, 5.7, 7.1, 7.3, 7.5.	See handout (LaTeX source).
PS03	Wed Feb 14	Mon Feb 19	Wed Mar 21	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	Wed Feb 28	Mon Mar 05	Wed Mar 21	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 07	Mon Mar 12	Wed Apr 25	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 (LaTeX source).
PS06	Wed Mar 14	Wed Mar 21	Wed Apr 25	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	Wed Apr 04	Mon Apr 09	Wed Apr 25	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 11	Mon Apr 16	Mon May 14	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 (new version of #6, LaTeX source).
PS09	Wed Apr 18	Wed Apr 25	Mon May 14	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 04	Mon 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 11	Mon 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.

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 (Mon May 21, 9:45am-noon).
• Grading: Final course grades consist of:
  

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