Math 310-0101: Introduction to Proof in Analysis
Mathematics is a beautiful subject, unique in that once a result is established it is true forever. These
results are established by mathematical proofs, and this course will introduce you to theorems and examples and
show how they are validated by proofs. I hope you will
find these results interesting and beautiful, and that you will study the proofs
as models for how to do the exercises.
Success in Math 310: The primary objective of this course is for students to become familiar with the langauge of mathematics, and to use that language to make mathematical proofs. There are weekly exercises, and they all ask you to solve problems and to prove that the solution is correct using the definitions and theorems you have learned in class.
The course will cover most of the material in the online textbook as outlined in the syllabus.
To succeed, you need to :
i) hand in each homework.
ii) ask questions in class, in office hours, or by email when you do not understand something. My contact information is given in the syllabus (see link below)
iii) Make sure you understand the definitions, so that you can understand the questions you are asked and the material presented in class.iv) Master the various proof techniques, as you will need to be able to use them on homewrork assignments and tests.
i) Each class will start with a question period, and students are encouraged to bring questions to raise in class! Questions may deal with previously handed homework, or with any other part of the material of the course! I will only begin the lecture after all questions have been answered.
ii) I will be in my office and available to you during my posted office hours: MWF 2 PM to 4 PM
iii) I will also respond to email questions, and this can lead to an interactive discussion.
The Text: This is
available online. The content of the course will be
taken entirely from the text. The exercises in the text ask you to
prove statements, construct examples, and answer questions. In each
case you are expected to provide a rigorous proof, either of the
statement, or that your example does what it is supposed to do, or that
your answer is correct.
Tests and Exam: There
will be three term tests and a final exam. All the questions on these
will be taken from the exercises in the text.