Math 322 reading, homework, and exam information

• You are expected both to attend lecture (and take notes!) and read the textbook. The lectures and textbook partly reinforce each other and are partly complementary. In particular, I will sometimes cover material in lecture which is not in the textbook, and you will sometimes be responsible for material in the textbook which is not covered in lecture.
• All homework assignments are due by 4 p.m. on the listed date, at my office. Late homework will not be accepted. If unusual circumstances arise and you contact me in a timely manner, then we can discuss alternative arrangements.
• Throughout this class, you need to explain your answers even when the problem doesn't explicitly ask for a proof; this typically means writing in complete English sentences. When deciding how much detail to include, here's the standard to keep in mind: your solution to a problem should be complete and clear enough that one of your classmates, who has paid attention in class but hasn't thought about that specific problem yet, could read your solution and understand exactly how it works. If you only try to convince the grader that you understand the solution, then you almost certainly won't write enough.
• The schedule below is tentative. Book sections may be adjusted depending on how quickly we get through material in class.

Final exam information

The exam will cover all the course material from the semester, aiming for even coverage of all the material. You will be asked for definitions of about ten of the terms on the lists of terms for the midterm exams.

I think I've repeated all the other information enough times to have made my point by now.

Exam 4 information

For good advice about studying, you should reread the article about study habits linked to from the syllabus. (Of course I know all of you already read it because it said to on the syllabus, but read it again to refresh your memory.) As a reminder, the most important point is to study actively — don't just read notes, do problems! But there's lots of other good information there, too.

The exam will cover all the course material from the semester, but the emphasis will be on material covered after the third exam, mainly on (classical) Fourier series. (But keep in mind the remark at the beginning of the solutions to exam 2.)

Definitions

You will be asked for complete, precise definitions of about four of the following terms, including context (e.g., what kind of thing might be differentiable?). Remember that a complete mathematical definition leaves no room for ambiguity: if you give me a definition of what it means for a function is differentiable, I need to be able to use it, in principle anyway, to decide whether or not any function I ever meet is differentiable. (The last part of the course was lighter on definitions than previous parts, which is why I'm including some terms which were also included on the last midterm and are relevant to the more recent material.)

• (complex) inner product space
• orthonormal system
• complete orthonormal system
• generalized Fourier series
• classical Fourier series
• Hölder continuous
• Fourier transform
• Fourier inversion theorem
• convolution

Keep in mind that you can't work with any of these concepts in a mathematically rigorous way without knowing the definitions — this is a list of the most important terms that you should know by heart anyway!

The rest

The rest of the exam will consist of several problems similar to homework problems. Rather than suggest new problems for review, I recommend you start with the homework and homework solutions, including problems that you got right and those that weren't graded. All the same important ideas you need to know for the exam were needed on the homework. After you've done the homework problems again, work on the dozens of exercises in the book which I didn't assign.

Finally, if you ask me how many problems there will be on the exam, I will point out that without knowing exactly how long and hard the individual problems are, the answer would not tell you anything. I expect most students to need most of the allowed time for the exam. (I also expect that by the time of the exam you should be able to do a given problem more quickly than you could have done it on the homework, when you were first working with the relevant ideas.)

Exam 3 information

For good advice about studying, you should reread the article about study habits linked to from the syllabus. (Of course I know all of you already read it because it said to on the syllabus, but read it again to refresh your memory.) As a reminder, the most important point is to study actively — don't just read notes, do problems! But there's lots of other good information there, too.

The exam will cover all the course material covered through April 4, but the emphasis will be on material covered after the second exam, starting with exterior derivatives and up to the completeness of the trigonometric system. (But keep in mind the remark at the beginning of the solutions to exam 2.)

Definitions

You will be asked for complete, precise definitions of about four of the following terms, including context (e.g., what kind of thing might be differentiable?). Remember that a complete mathematical definition leaves no room for ambiguity: if you give me a definition of what it means for a function is differentiable, I need to be able to use it, in principle anyway, to decide whether or not any function I ever meet is differentiable.

• exterior derivative
• pushforward
• pullback
• chain
• boundary of a cell
• orthonormal system
• complete orthonormal system
• generalized Fourier series
• classical Fourier series

Keep in mind that you can't work with any of these concepts in a mathematically rigorous way without knowing the definitions — this is a list of the most important terms that you should know by heart anyway!

The rest

The rest of the exam will consist of several problems similar to homework problems. Rather than suggest new problems for review, I recommend you start with the homework and homework solutions, including problems that you got right and those that weren't graded. All the same important ideas you need to know for the exam were needed on the homework. After you've done the homework problems again, work on the dozens of exercises in the book which I didn't assign.

Finally, if you ask me how many problems there will be on the exam, I will point out that without knowing exactly how long and hard the individual problems are, the answer would not tell you anything. I expect most students to need most of the allowed time for the exam. (I also expect that by the time of the exam you should be able to do a given problem more quickly than you could have done it on the homework, when you were first working with the relevant ideas.)

Exam 2 information

For good advice about studying, you should reread the article about study habits linked to from the syllabus. (Of course I know all of you already read it because it said to on the syllabus, but read it again to refresh your memory.) As a reminder, the most important point is to study actively — don't just read notes, do problems! But there's lots of other good information there, too.

The exam will cover all the course material covered through February 29, but the emphasis will be on material covered after the first exam, namely the material corresponding to sections 5.8 and 5.9 of the textbook (excluding the portions of 5.9 on exterior derivatives, pushforwards, and pullbacks).

Definitions

You will be asked for complete, precise definitions of about four of the following terms, including context (e.g., what kind of thing might be differentiable?). Remember that a complete mathematical definition leaves no room for ambiguity: if you give me a definition of what it means for a function is differentiable, I need to be able to use it, in principle anyway, to decide whether or not any function I ever meet is differentiable.

• grid
• Riemann sum
• upper/lower sum
• upper/lower integral
• Riemann integrable
• Darboux integrable
• measure zero
• k-cell
• basic k-form
• simple k-form
• k-form
• ascending presentation
• wedge product

Keep in mind that you can't work with any of these concepts in a mathematically rigorous way without knowing the definitions — this is a list of the most important terms that you should know by heart anyway!

The rest

The rest of the exam will consist of several problems similar to homework problems. Rather than suggest new problems for review, I recommend you start with the homework and homework solutions, including problems that you got right and those that weren't graded. All the same important ideas you need to know for the exam were needed on the homework. After you've done the homework problems again, work on the dozens of exercises in the book which I didn't assign.

Finally, if you ask me how many problems there will be on the exam, I will point out that without knowing exactly how long and hard the individual problems are, the answer would not tell you anything. I expect most students to need most of the allowed time for the exam. (I also expect that by the time of the exam you should be able to do a given problem more quickly than you could have done it on the homework, when you were first working with the relevant ideas.)

Exam 1 information

For good advice about studying, you should reread the article about study habits linked to from the syllabus. (Of course I know all of you already read it because it said to on the syllabus, but read it again to refresh your memory.) As a reminder, the most important point is to study actively — don't just read notes, do problems! But there's lots of other good information there, too.

The exam will cover all the course material covered through February 8, namely the material corresponding to sections 5.1–5.5 and 5.7 of the textbook.

Definitions

You will be asked for complete, precise definitions of about four of the following terms, including context (e.g., what kind of thing might be differentiable?). Remember that a complete mathematical definition leaves no room for ambiguity: if you give me a definition of what it means for a function is differentiable, I need to be able to use it, in principle anyway, to decide whether or not any function I ever meet is differentiable.

• linear transformation
• matrix representing a linear transformation
• operator norm
• differentiable
• (total) derivative
• partial derivative
• Jacobian
• second derivative
• Hessian
• k^th derivative
• C^k function
• gradient

Keep in mind that you can't work with any of these concepts in a mathematically rigorous way without knowing the definitions — this is a list of the most important terms that you should know by heart anyway!

The rest

The rest of the exam will consist of several problems similar to homework problems. Rather than suggest new problems for review, I recommend you start with the homework and homework solutions, including problems that you got right and those that weren't graded. All the same important ideas you need to know for the exam were needed on the homework. After you've done the homework problems again, work on the dozens of exercises in the book which I didn't assign.

Finally, if you ask me how many problems there will be on the exam, I will point out that without knowing exactly how long and hard the individual problems are, the answer would not tell you anything. I expect most students to need most of the allowed time for the exam. (I also expect that by the time of the exam you should be able to do a given problem more quickly than you could have done it on the homework, when you were first working with the relevant ideas.)

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