The topics covered in the calculus part include partial derivatives, gradients, Lagrange multipliers and multiple integrals.
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At the exercise sessions the students will solve and present solutions to mathematical problems. The mandatory assignments are of the form of mathematical problems. The solutions must be submitted in written form. The student will receive the grade NA not approved at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt. The exam is a 4 hour written exam 1. Solutions submitted hand written on paper. Access to aid in the form of books, own notes, e-books, also on laptops and iPads is permitted.
Use of internet including email and social media is not permitted. Any form of communication between students or with the outside world is not permitted.
Skip to main content. Side panel. You are not logged in. Log in. Autumn Autumn Autumn Course info. Magnus Baunsgaard Kristensen ,. Loisa Roma Taylor ,.
Patricija Bautrenaite ,. Lars Reiter Nielsen ,. The exercises also seem independent. For instance, I did not find any places where an exercise relies on you having completed an exercise from an earlier section, which is very nice from the standpoint of modularity. I have seen other reviewers complain about the length of the text, but I think this may be a consequence of having a text that is so modular, and also inclusive of advanced topics.
I would much rather have a long text from which I can extract the pieces I need, than a short text with topics all mashed together. I think the author was wise to trade brevity for modularity in this book. This text has a clean, clear development of linear algebra. This seems to me to be a very reasonable way to build things up. I think it really is a nicely organized text, with easy-to-find topics, a carefully layered build-up of topics, and with the main topics cleanly separated.
I had no problems navigating the pdf. Both text and graphics appeared very clear, rendered immediately, and were easy to read. This is a book on abstract mathematics, and as expected, no material arises that would reasonably be considered to be ulturally insensitive or offensive. Very nice book, and I am considering using it in a classroom, but I wish it had a little more of a nod to the difficulties of handling large matrices. For a classically-focused course though, the book is excellent. For the book's stated purpose of providing a first approach to linear algebra is met. The rigor is appropriate and the author has gone to great lengths to cover the standard definitions, theorems, and examples that are at the heart of linear The rigor is appropriate and the author has gone to great lengths to cover the standard definitions, theorems, and examples that are at the heart of linear algebra.
The author has done an exceptional job providing a modern exposure to linear algebra that is accessible to students of all STEM disciplines. The applications are appropriate for the audience and the theory of linear algebra will not become obsolete in the next twenty years.
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Consider the following passage from an example on row reduction: "Notice that the first column is nonzero, so this is our first pivot column. The first entry in the first row, 2, is the first leading entry and it is in the first pivot position. This style is consistent throughout the text and technical terminology is properly used. I am also happy to say that the author sets a fine example of never abusing notation. This book provides a consistent and mature approach to the topics in each section. In particular, the final section on vector spaces is written at a level that is appropriate for students that want to take a deeper look at the underlying frameworks of linear algebra.
The challenge in a linear algebra text is that there are so many definitions to cover in order for the abstract theory to develop. The first few section of the book, , are essential. However every topic in sections need not be assigned. For example, section 2. Once the first 4 chapters are covered it is trivial to reorder the later sections to fit the objectives of your own course.
Students at this level should have no problem filling in the small gaps caused by any reordering. Each section provides simple, leading examples that explore the new topic. Theorems, and when necessary, their proofs are presented in a logical fashion. There are a sufficient number of examples for each section covering the basic ideas and cases that one encounters in linear algebra. Theorems, examples and figures are clearly denoted throughout the textbook.
The use of color is also consistent and makes it easy to skim the sections. I appreciate that learning outcomes are well organized and appropriate for each section. I would suggest adding a link in the table of contents to the exercise section of each chapter. This book's style and grammar is consistent with the books found from the major textbook publishers. This book does not cover any topics about culture, race or ethnicities and is written in a respectful manner.
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I have taught from the author's related book, "Elementary Linear Algebra", and I find the refinements here of the material to be a positive change in every regard. This book is an excellent example of a mature textbook for students in STEM fields. The book is sufficiently comprehensive for its purpose as a first course in the subject. The row reduced echelon form and its many consequences and applications are covered well in the first several chapters.
Later chapters on linear Later chapters on linear transformations and spectral theory are presented at a nearly ideal level for such a course and a reasonable selection of applications are included. Aside from a few minor typographical errors the content appears to be very accurate.
No substantive errors were noted.
The book is written in a very conversational style, and for the most part this aids the presentation. Dense paragraphs are mostly avoided and the text is broken up with examples, theorems, etc I found no inconsistencies aside from a few minor issues with incorrect references to theorem numbers ex. The length of individual sections is reasonable and topics are as self-contained as they can be given the nature of the subject.
The order and presentation of topics are quite clear, with plenty of examples. As noted by another reviewer, the overall length of the text may seem excessive to some readers. The small number of figures in the text serve their purposes well. Overall, the text is very easy to navigate and visually attractive. This book contains all of the material that would generally be covered in a Freshman or Sophomore Linear Algebra course. The section on vectors is quite extensive, and would be excellent to use in a Freshman course that needed to introduce vectors The section on vectors is quite extensive, and would be excellent to use in a Freshman course that needed to introduce vectors very early for use in Engineering courses.
On the other hand, the sections on Linear Transformations and Eigenvalues are exactly what I would want to see in a Sophomore course that was designed more for mathematicians. The section on abstract vector spaces I find somewhat deficient for a more theoretical course.
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The content is fully accurate. The theorems and proofs that are provided in each section are presented with precision, and yet easy to read. The fundamental courses of mathematics are not generally given to change, but Linear Algebra perhaps more than the rest does need to keep itself updated with the rapidly changing field of Numerical Analysis.
I think that Kuttler has done an excellent job of keeping up with the current methods, but has not written in such a way as to make the text dependent on any particular numerical methods that are in vogue. I like very much the style of writing and even the formatting of headers and content titles. I found it very readable and easy to find what I was looking for. I did not detect any inconsistency in the way that the material was presented.
The only thing that might be considered an inconsistency is that Subspaces and presented in the text prior to vector spaces.
It is somewhat unnatural to define the subspace of something that is not defined as yet, but sadly it has become somewhat commonplace to do things in this way. The sections of the book are easily adaptable. I did like the fact that the section on vector spaces was written in a way to be included earlier if desired.
Other than this issue with the section on vector spaces, I found the organization and flow of topics to be quite natural. Each topic comes in its proper place, but not in such a way as to detract from its adaptability. I like the way that sections and headings and theorems all are very descriptive, but also numbered, so that they can be easily found.
Exercises are provided at the end of each major section, and I found them to be ample both in quantity and in terms of the level of difficulty. In my experience, text book works extremely well with the learning outcomes defined by my institution for entry level linear algebra course.
For my students, textbook provides a foundation for the course. Techniques to solve the problems are easy Techniques to solve the problems are easy to follow and build upon as the topics gets harder. Text stays consistent throughout with definitions, solutions and responses. Students get used to the pattern of solving the problems.