LINEAR ALGEBRA AND APPLICATIONS (4 semester hours) Matrix algebra and solutions of systems of linear equations, matrix inversion, determinants. Vector spaces, linear dependence, basis and dimension, subspaces. Inner products, Gram-Schmidt process. Linear transformations, matrices of a linear transformation. Eigenvalues and eigenvectors. Applications. Constructing and writing mathematical proofs. A transition between beginning calculus courses and upper-level mathematics courses.
PREREQUISITE: Math 232
SYLLABUS The course will cover most of Chapters 1-7 of the text.
Note that many institutions offer very good Matrix Theory classes, typically for 3 credit hours, but that these cannot be used to substitute for MATH 240 because they do not have the necessary level of abstraction and the expectation that the student learn to work with axioms and proofs. If you expect to transfer a linear algebra course to NIU please contact us before taking the course to evalute its suitability as a replacement for MATH 240. (Two community colleges whose Linear Algebra courses do articulate as NIU's Math 240 are those at Heartland and McHenry County Community Colleges.)
WITHDRAWAL: The last day for undergraduates to withdraw from a full-session course is Friday, March 10, 2006.
SAMPLE EXAMS:
Typical Math 240 exams involve non-routine calculations. You may
wish to look at some exams from previous semesters to see the
level of analysis we expect students to be able to carry out.
In particular, you should expect that only half of the verbs in
the final exam will be "compute", "calculate", or "find"; the others
will be "prove", "show", or "explain".
Fall 2004 final
Fall 2002 final
[Adobe's Acrobat Reader (free download)]
Please note that these exams are not necessarily comprehensive, and thus there are topics which were not included on these exams which may be tested on your final exam.
Your own instructor will write and grade your midterm exams and will grade your final exam.
FINAL EXAM: The final exam will be a comprehensive, departmental examination. All sections of this course will take the same final exam at the same time: Thursday, May 11, 2006; 8-9:50 A.M. The exam will probably NOT be in your regular classroom. Room assignments are usually made one to two weeks before the final exam week.
CALCULATORS: No calculator nor computer software is required for this course: this course is oriented away from computational matters. To check their homework, students might sometimes like to have access to calculators or computers that can solve systems of linear equations and manipulate matrices. However, no electronic devices will be allowed on final exams. Your instructor may further regulate the use of calculators on the hour exams.
TEXT:
Elementary Linear Algebra (8th ed.),
by Bernard Kolman and David R.Hill,
published by Prentice-Hall, Upper Saddle River, New Jersey, 2004.
(This is NOT the book "Introductory Linear Algebra" by the same authors.)
Some additional references:
ACADEMIC CONDUCT: Academic honesty and mutual respect (student with student and instructor with student) are expected in this course. Mutual respect means being on time for class and not leaving early, being prepared to give full attention to class work, not reading newspapers or other material in class, not using cell phones or pagers during class time, and not looking at another student's work during exams. Academic misconduct, as defined by the Student Judicial Code, will not be treated lightly.
CAAR STATEMENT: If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let your instructor know early in the semester so that your learning needs may be appropriately met. You will need to provide documentation of your disability to the CAAR (Center for Access Ability Resources) Office located in the Health Services Building, 4th floor.
ASSESSMENT: If you are a mathematical sciences major, your final exam will be retained as part of the department's ongoing program assessments.
You may decide by the end of the semester that this wasn't a course in mathematics as you used to understand it; it's more like a course in communication!
This course is for most students the first one which requires working with axiomatic structures, and that is what makes this course both difficult and essential. You will need to master certain computational skill, and most students do that well.
But you will also need to memorize mathematical definitions; this is not hard but you may be unaccustomed to it. (Try writing out flash cards and spending some time every day memorizing the definitions word-for-word.) And you will also have to get used to understanding a mathematical definition --- what are some examples of the term? what are some non-examples? how is the term used?
Likewise you will have to memorize axioms. It isn't really necessary to memorize these word-for-word but that's the safer thing to do -- otherwise you might forget a little word like "not" which would change the whole meaning of the axiom. You have even a little more latitude with the theorems -- you certainly have to remember what they say, but saying it in your own words can be a valuable exercise.
You don't have to memorize the proofs you see. However, you are expected to learn how to do your own proofs, so it really pays to read and think about the proofs in the book. How does the author make them work? When does a proof by contradiction get used? Which previous theorems are being used in this proof? Would the proof still work if one of the axioms wasn't assumed? If you read only half the proof and then closed the book, could you think of how to finish the proof on your own?
If you are a math major you will definitely be taking Math 430 and probably Math 420 and other proof-based courses in the future -- maybe even next semester. These courses are All Proofs All The Time, so you need to take this semester to ease into that idea. You'll eventually see that the definition-theorem-proof mode of thinking about abstract ideas like mathematics is very natural and very useful; this is your chance to start to see why.
It really pays to work closely with your instructor for this kind of course. Take advantage of his or her office hours and go in for a little chat. The right question is usually not, "How do you do number 6?" but rather "Can you give me an example that shows what this definition means?". Many students find that study groups help too --- you'll have a chance to have such conversations with other people whose understanding is right about at your level.
Students who successfully complete this course have completed at least two-thirds of the requirement for a minor in Mathematical Sciences; by taking a 300-level course (such as MATH 336 or STAT 350) and virtually any 400-level course, they can complete the minor. Students who do well in this course and will be at NIU for several more semesters are urged to consider a major in our department (possibly in conjunction with another major). Please see an academic advisor to discuss your options in this department.
Last update: Jan 13, 2006