UC Berkeley Math 104
Introduction to Analysis

Homework

Exam-related handouts

A note about writing

If you read any textbook or scientific article, you will see that there is a standard way of writing mathematics, in which equations form part of full sentences and occur naturally with the flow of the text. While completely optional, Math 104 is a great place to practice this in writing your homework. In general, the solutions posted here try to adhere to this standard.

One way to write mathematics like this is to make use of the free software package LATEX, which can produce very high quality scientific documents, and is used extensively by mathematicians, physicists, and engineers. There is an excellent guide, The Not So Short Introduction to LATEX2ε, which can be used to get started. The homework assignments and solutions are all written in LATEX. Some sample LATEX files are available here:

• LATEX source for homework 1
• LATEX source for homework 1 solutions

Additional notes and handouts

• Prof. George Bergman's notes on set notation – these notes go into detail about set notation and logic, and discuss the use of the logical quantifiers “for all” and “there exists”, which are used frequently in this course. They also provide a number of short exercises.
• A discussion about taking limits (PDF | PS) – this document highlights a potential pitfall with applying limit theorems on question 6 of homework 2.
• Strategy for Testing Series – These notes from James Stewart's Calculus describe various techniques for determining which convergence test is most appropriate for a given series. The notes have numerous examples that are good practice for the first midterm.
• A space-filling curve (PDF | PS) – this document shows how the concepts learned in the class can be used to construct a continuous mapping from the unit interval onto the unit square.