A pdf version of this content is available: Syllabus
Math 313 will cover the basic properties of real numbers, with
special emphasis on completeness of the real numbers, and a rigorous
development of Calculus through the fundamental theorem with
attention paid to limits, continuous functions, differentiability,
and the Riemann integral. Although the material is familiar, the
point of view is different as we will accomplish our goals in a
mathematically rigorous way beginning with a few basic notions.
Mtht 490, Analysis I for Teachers
is a required extension to Math 313 for BST majors. It meets Tuesday
12:30 - 1:45. We will be exploring topics more deeply through
problem solving. All Math 313 students are invited to attend.
Mtht 490 extends the material to cover connections with teaching high
Prerequisite(s): Grade of C or better in MATH 215. Students will be
writing proofs and inventing interesting examples throughout this
course. Experience in Math 215 is invaluable for success and
required to enroll. See the instructor for exceptions.
Interactive Notes for Real Analysis
by Bonnie Saunders, 2015.
You will want to have a copy of the first chapters by the
second meeting of class. Download here: Chapters 0 and 1
Here is a pdf of Chapter 2, which we will start in class on
September 28. Download here: Chapter 2
Here is an uptodate version of the entire set of Notes, including
updates to Chapters 0 and 1 as inspired by the work we have done
so far in class. Chapters 3 - 5 are still very much in
for class. Download draft here:
Chapters 1 - 5
Suggested other reading:
Understanding Analysis by Stephen Abbott, 2010, which is available online through the UIC Library.
This is a free online system for collaborative writing using Latex. Students will use this tool to complete
team assignments. Details will be supplied in class. No knowledge of LaTex is required for the class.
Students are welcome to use a laptop during class. We
will be making some use of Geogebra. This free, downloadable
software is a combination of a graphing calculator, a spreadsheet
and something similar to geometers sketchpad.