| Instructor: | Dr. Douglas Anderson |
| Ivers 234G | |
| 299-4453 (office), 299-4151 (math department) | |
| andersod@cord.edu |
Office Hours: TuTh 1:00-4:00, other times by discovery.
Academic Integrity: The students and faculty of Concordia College are committed to the expectations and procedures set forth in the joint statement on academic responsibility. Academic honesty is expected of all students at all times. Dishonesty (for example, cheating or plagiarism) will result in a minimal penalty of failing the exam or assignment in question. Some offenses constitute grounds for failing the course.
Text: Linear Algebra: a Modern Introduction, 2nd edition, by David Poole, ISBN 0534998453.
Prerequisite: Math 122 (Calculus II) or equivalent.
Purpose: There are many ways to study linear algebra. For example, we could focus on computational matrix algebra and its applications to calculus, differential equations, the physical and social sciences, economics, and so on. Or we could concentrate on the broader topic of linear theory and general vector space structure. These and many other approaches could easily fill several semesters of study. Having only one semester at hand, we will strike a balance between mathematical reasoning on the one hand, and linear systems and vector spaces on the other; a few applications will be done as time permits. With nearly half of our emphasis being theoretical in nature, we consider this course to be the first real transition course to mathematical proof. The reliance on rational, rigorous proof is a hallmark and strength of mathematical inquiry, a reliance we will develop and expect in this course. By studying the mathematical vocabulary and the logical structure of the foundation of linear algebra, we learn the fundamental logic of deductive and inductive reasoning; encounter and construct proofs of elementary theorems using direct, indirect, existence, and inductive arguments; and understand the role of mathematical definitions and counter examples. Topics in linear algebra include systems of linear equations, matrices, determinants, vectors in n-space, abstract vector spaces, and linear transformations.
Homework: Homework will be assigned (even-numbered problems) each day for your development toward mastering
the material, and will be due two class periods later. I will allow up to four (4) late submissions without penalty;
after that late homework will not be accepted. Your final homework write-up must be neat and organized. You will
not only be graded on correct answers but also on the neatness, organization, steps used to derive your answers, and
the use of correct English grammar and complete sentences. All students must abide by Concordia College's
expectations regarding academic integrity and quality.
Exams: Attendance is required for all exams. If you should miss an exam for an emergency you
will be allowed to make it up only if you have notified me before the exam and it
must be made up in a timely manner (to be discussed with me individually). I will give you at
least one week notice before the exams. The comprehensive final exam is scheduled for
8:30-10:30 a.m. Wednesday, April 26.
Grading: With a total of 650 points, the course grades will be as follows:
|
A A- B+ B B- C+ |
598-650 |
C C- D+ D D- F |
468-496 |
|
Homework Exam 1 Exam 2 Exam 3 Final Exam |
150 |
every class |
| Date | Section | Exercises |
| Jan 4 | 1.1 Geometry of Vectors | (13) 5bc,7-12,14,19-22 |
| 6 | 1.2 Vector Dot Product | (26) 1-3,7,8,13,14,24,25,30,35,36,42-44 |
| 9 | 1.3 Lines and Planes | (41) 2-4,11-14,21,22,24,27,28,32,41 |
| 11 | Intro to Proof I | Handout; (27) 46a,53-59,61-64 |
| 13 | 1.4 Code Vectors | (53) 1-13 odd,19,21-27 odd,37,41,45,53 |
| 16 | Intro to Proof II | Handout |
| 18 | 2.1 Systems of Equations | (64) 21,22,27,31,34-37,40-42 |
| 20 | 2.2 Solving Linear Systems | (83) 13,14,26,27,30,36,37,40-42,45,46,49 |
| 23 | Review | (56) 1a-h,2-10,12-15; (132) 1a-d,3,4,7-9,16,20 |
| 25 | Exam 1 | |
| 27 | 2.3 Span and Independence | (99) 3-5,7-10,15,16,23-25,27,28,42,43,48 |
| 30 | 3.1 Matrix Operations | (150) 1,4-9,14,19,20,30,33,37,38 |
| Feb 1 | 3.2 Matrix Algebra | (159) 3,4,6,10,13,14,22,26,29,37,40 |
| 3 | 3.3 Matrix Inverse I | (176) 1-4,6,9,14,17,19,20-23,38 |
| 6 | 3.5 Subspace and Basis | (207) 1-6,12a,14,19,23,28,29 |
| 8 | 3.5 Dimension and Rank | (208) 18,37,39-43,46,47,52,55,64 |
| 10 | 3.3 Matrix Inverse II | (177) 44,46,51-55 |
| 13 | 3.6 Linear Transformations | (221) 1,5,7,13,15,17,21,23,25,37 |
| 15 | Review | (132) 1e-j,10-17; (250) 1abcghij,2-6,8,9,11,13-16,18,19 |
| 17 | Exam 2 | |
| 20 | 4.1 Eigenvalues and Eigenvectors | (259) 1-5,7-9,12,13,15,19,21,24,27,36 |
| 22 | 4.2 Determinants | (280) 1,4,7,8,12,14,16,47,48,52-56 |
| 24 | Spring Break | No Class |
| Mar 6 | 4.2 Determinants | (281) 26,27,30,35-40,45,46 |
| 8 | 4.3 Eigenvalues and Eigenvectors | (295) 3-6,10,17-23,25 |
| 10 | 4.4 Similarity and Diagonalization | (306) 1,5,8-11,20,24,25,31,33,34,40-42 |
| 13 | 4.6 Applications | (244) 1-4,10; (356) 1-4,7,8,10 |
| 15 | 5.1 Orthogonality | (373) 1-6,9,10,14,17,20,22-24,35 |
| 17 | 5.2 Orthogonal Complements | (384) 1,2,6,8,10,15,16,19,20 |
| 20 | 5.3 Gram-Schmidt Process | (391) 1,2,5,6,7,8 |
| 22 | Review | (362) 1,2,4,6,7,9-12,16-20; (429) 1-7,9,11,13,14; (632) 13,14 |
| 24 | Exam 3 | |
| 27 | 7.3 Least Squares | (595) 7,8,15,32 |
| 29 | 6.1 Vector Spaces and Subspaces | (445) 1,3,5,7,9,24-26,30,31,34,38,40,41,45,62 |
| 31 | 6.2 Independence, Basis, Dimension | (460) 3,8,17,20-22,34,37,46,52,54 |
| Apr 3 | 6.3 Change of Basis | (475) 1,4,11,16,21 |
| 5 | 6.4 Linear Transformations | (484) 1,2,3,6,7,9,15,18,22,24,35 |
| 7 | 6.5 Kernel, 1-to-1 Transformation | (499) 1,3,5,7,9,13,15,17,19 |
| 10 | 6.5 Range, Onto Transformation | (499) 21,27,31,33,37 |
| 12 | 6.6 Matrix of Transformation | (516) 1,5,7,13,17 |
| 14 | Good Friday | No Class |
| 17 | Easter Monday | No Class |
| 19 | 6.6 Matrix of Transformation | (516) 19,23,31,35 |
| 21 | Review | (536) 1-4,7-12,14,18 |
| 24 | Review | Exams 1-3 |
| 26 | Final Exam | Wednesday, 8:30-10:30 |
Key Equivalences in Linear Algebra: Let A be an nxn matrix.
|
A inverse exists A is invertible A is nonsingular A(A inverse) = (A inverse)A=I rref(A)=I, A and I are row equivalent A has n (nonzero) pivots Ax=0 has only the trivial solution Ax=b has unique solution x=A^(-1)b Determinant of A is nonzero Rows of A are linearly independent Row space of A is R^n Rank(A)=n Columns of A are linearly independent Column space of A is R^n Nullity of A is 0 All eigenvalues of A are nonzero |
A has no inverse |