Brian Van Koten
Assistant Professor
Email: vankoten(at)math.umass.edu
Office: LGRT 1428
Website: See my personal website
here.
If you have questions or concerns, talk to me during my office hours or make an appointment. My office hours are listed on my math department directory page.
I may change my office hours during the course of the semester. Any such changes will be announced in advance in class.
Lectures will be held MWF from 1:25-2:05pm in LGRT 1114.
Homework may be assigned after any class. There will be at least one assignement given each week. All assigments will be posted below. Problems assigned during each week will be due the following week on Friday.
No late homework will be accepted. Instead, when the total course grade is computed, the lowest homework score will be dropped.
I encourage you to discuss the homework with your classmates and to come to my office hours with your questions.
The midterm exam will take the form of a special assignment given around Halloween. Students will have one week to complete this assignment.
Please do not discuss the problems on the midterm with anyone. You may consult any of the recommended texts, but please do not search the web for solutions.
If for any reason you will not be able to take either exam at the specified time, let me know as soon as possible.
If you suspect that a mistake has been made in the grading of your work, please point it out to me no more than two weeks after the work was returned. I will not consider complaints if more than two weeks have passed. Please do not ask the grader to change homework grades; come to me with any disputes.
You may find the texts listed below useful. When available, I will give references for results discussed in class, usually in one of the sources below. I will also post excerpts from my lecture notes from time to time, as needed.
Kincaid and Cheney. Numerical Analysis: Mathematics of Scientific Computing.
Clear explanations of theorems and algorithms with all details.
Quarteroni, Sacco, Saleri. Numerical Mathematics.
An overview of numerical analysis written from a contemporary perspective. Excellent for its broad and philosophical view of the subject and its examples. I recommend this book if you want to understand how the whole of numerical analysis fits together and if you want to know the fundamental strengths and limitations of various classes of methods. However, many results are stated without detailed proofs.
This book is available on-line from the library.
Trefethen and Bau. Numerical Linear Algebra.
This books covers only linear algebra. Proofs are very clear and detailed, although the component pieces of a result are sometimes scattered throughout several different chapters. More a collection of lectures than a conventional book, so might be frustratingly disorganized and incomplete as a reference.
Golub and Van Loan. Matrix Computations.
An impressively concise and scholarly reference for numerical linear algebra with an extensive bibliography. If you just want the facts without all the digressions and explanations in Trefethen and Bau, this is a great book.
Introductory courses in analysis and linear algebra. Competency in computer programming. Students should be prepared to learn elements of ordinary and partial differential equations, probability, data science, physics, and engineering, as needed.
I recommend that all students use Python. However, in principle, I will accept correct programs written in any language. I have listed all of the reasonable choices roughly in order of preference.
I think you will probably want to use either the Spyder IDE or Jupyter Notebooks for this class. Spyder is more versatile and it is probably easier to learn. Jupyter might be better for our purposes, however, because you can do both the code and the write up together in Jupyter.
I have been unable to find a good tutorial for Spyder, so I will simply give a demonstration in class. It is quite similar to the MATLAB IDE and also RStudio. Spyder comes with decent documentation, so I don't think you will have any trouble picking it up.
Turn in your programs as appendices to your assignments. If you prefer, you may instead turn in jupyter notebooks incorporating both code and explanations.
The total course score will be computed according to the following formula: 50% Homework + 30% Midterm + 20% Final.
If your score is in the top third, you will receive an A. If your score is in the middle third, you will receive at least a B, but possibly a higher grade. If I am convinced that all students understand the basic principles of the course, I will not give any C's, D's, or F's. I will make the distribution of scores on the midterm and the final exam known.