MTHT 430 Fall 2014
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 school mathematics.
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.
Course text: 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 draft form. 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.
Overleaf 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.