UCSB Summer B 2016: Math 117

Office Hours will be held in SH 6432U at the following times:

  • Week with no exams: R 10am-12pm, F 12pm-2pm
  • Week with exams: T 10am-12pm, W 10am-12pm

Check your syllabus for which week exams are held (typically every other week). You may also email me at vtkala@math.ucsb.edu for a short appointment outside of office hours.

August 10

How I study for analysis exams:

  • Memorize all definitions and statements of theorems theorems.
    • I like to make flash cards:
      • For definitions: On one side right the word that is being defined, i.e. “Bounded sequence”. On the other side, right the definition using mathematical language, i.e. “There exists an M > 0 such that…”
      • For theorems: On one side, ask your self a question related to a theorem, i.e. “How are convergent and bounded sequences related?”. On the other side, answer the question with the theorem, i.e. “Convergent sequences are bounded.”
    • I will then write down the definitions a few times from memory and check to see if they are correct.
  • Review homework
    • I don’t suggest memorizing the solutions word for word, but I do recommend memorizing the steps you used to solve it. For example, you had a problem on the homework that stated “xy = 0 if and only if x = 0 and y = 0”. How I would break it down in to steps:
      • Two directions
      • First direction: Suppose xy = 0, but x nonzero, y nonzero. Use multiplicative inverses.
      • Second direction: Plug in x = 0, then y = 0.
  • Review proof of theorems done in class
    • Again, don’t memorize the proof verbatim, but try to memorize the steps.
  • If extra time, try some problems in the text.

From experience, I expect that there will be problems associated with your previous homework and with every major definition. Definitions are your best friend, know them and know how to use them.

August 2

Download LaTeX:

For both PC and Mac I recommend the editor TeXMaker. Here is a screenshot of how it looks on my Mac:


Don’t want to download? No problem! You can use a free online editor at: https://www.overleaf.com. It is accessible from anywhere, even your iPad! They have several layouts to choose from, you do not need to use the layout I created.

Here is a sample homework file as promised:

  • samplehomework.tex, this is the .tex file, it is only code and will need to be opened up via your editor (only works if you have downloaded LaTeX onto your computer)
  • samplehomework.txt, this is the .txt file and can be copied and pasted into your editor (use this if you are using an online editor, you can also use if you have downloaded LaTeX onto your computer)
  • samplehomework.pdf, this is what the output file should look like

** Edit April 14, 2019 : I no longer have these templates available, I now exclusively use Overleaf which has oodles of templates available **

You are welcome to use this sample file for your homework, but of course I recommend creating your own layout. You can use a search engine to get some inspiration (i.e. “sample homework files LaTeX”).

There are several online tutorials for LaTeX, just use a search engine (i.e. “LaTeX tutorial”). You can use a search engine for what you are looking for as well (i.e. “how to make matrices in LaTeX”).