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.

Course material:

            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 am committed to helping each student through this process. In particular,

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.
 

          Homework: The course will include regular homework assignments, assigned by email and/or on the course homework webpage, and a selection of questions               will be graded.  All the homework problems will be taken from the exercises in the text. 

 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.

              Syllabus

  Text

  Homework, Midterms, and Exam