Course Description 
About Exam:
We will have two remote openbook exams. The midterm is on 8/20, 2:20 pm to 5:20 pm, and the final exam is on 8/30 from 2:20 pm to 5:20 pm. Each exam accounts for 50 \% of the final grade. The midterm exam includes material from the first four lectures (8/98/16), and the final exam covers the rest. If you just want to audit the class, you don't have to take the exams.
Around half of the exam questions will directly come from homework, so solutions for these exercises are unavailable. Instead, I will give you hints to lead you through constructing a proof. Another half of the exam questions will test your understanding of definitions, how to correctly apply a theorem, why we need assumption xxx to develop a theorem, and algebra problems.
About Course:
This is a mathematical analysis course for doctoral and master students in economics. The course is designed for students with weak math background but are required to take 3 core courses in graduatelevel in the coming fall; I do not ask too much of your math skills, although some familiarity in calculus and linear algebra are expected.
Analysis is an important skill if you want to read graduatelevel economic textbooks and write economics paper. From delivering a concise message, applying a theorem correctly, writing/understanding a proof, or even simply reading a paper without misunderstanding the authors, you need analysis. My experience is that analysis skill is not something you can acquire within a short time. You need time to get familiar with it, use it, and then finally internalize it. That is to say, if you are a beginner, it is completely normal to find this course hard.
The textbook for this course is ``a first course in optimization theory” by Sundaram. It is needless to say how important the applications of optimization theory in economics! Since we only have three weeks, I will only cover chapter 1 of Sundaram’s book, which are mathematical prerequisites to study optimization theory. I use Apostol’s book as a reference book to define concepts, state theorems, and teach proofs. After the course ends, you still have 3 weeks to read Chapter 28 of Sundaram’s book. With good understandings in Chapter 1, I am sure that you will find the rest of the book not difficult to read.
There are two versions of lecture notes, labelled by white and blue. The white version is like a worksheet, which is for you to practice stating a definition/ writing a proof. If you feel uncertain, you can check the blue version of lecture notes.
Just in case you don't know: notation is to introduce symbols; definition is to define a new concept; theorem is to be proved by logics, using definitions or theorems previously proved.
