MTH 435 and its second part MTH 436 provide an introduction to the wonderful world of real numbers,
real analysis and topology. Real analysis is the precise mathematical theory behind Calculus.
The emphasis will be on mathematical precision and developing strong skills in proving theorems.
You will see complete proofs done in class and learn how to write your own proofs. At the same time,
you will gain a deep understading of the fundamental concepts of Calculus
that you already know from the intuitive point of view. Those include limits, continuity, sequences of numbers and differentiation.
Many theorems in analysis that we will prove are particular cases of more general theorems
in metric spaces. Therefore, we will study metric spaces which belong to the area of mathematics called topology.
You will find here current downloads: solutions to homework problems, additional class notes etc.
Homework 1 Solutions
Homework 2 Solutions
Homework 3 Solutions
Homework 4 Solutions
Homework 5 Solutions
Homework 6 Solutions
Homework 7 Solutions
Homework 8 Solutions
Homework 9 Solutions
Exams and Evaluation
There will be two exams during the semester, Friday Oct 17, 3-5 and Friday Nov 21, 3-5, Lippitt 204.
Our Final is scheduled (by the Office of Enrollment Services) on Fri, Dec 12, 3-6pm, Lippitt 204.
Final Exam Schedule.
Your grade will be based upon a possible total of 550 points, as
- Exam 1 -- 100 points,
- Exam 2 -- 100 points,
- Homework -- 150 points,
- Final exam -- 200 points,
Weekly homework will be assigned in class.
The Completeness Axiom
Density of Rationals and Irrationals
Countable and Uncountable Sets
SEQUENCES OF REAL NUMBERS
Intervals, Neighborhoods, the Triangle Inequality
Convergence, Divergence, Limits
The Bolzano-Weierstrass Theorem
Intermediate Value Theorem
Proofs of the Product, Quotient, Chain Rules
Mean Value Theorem
Monotonicity and the Derivative
Open and Closed Sets
The Real Line as a Metric Space
Sequences in a Metric Space