MATH 3130

SYLLABUS AND HOMEWORK

Mathematics 3130

Introduction to Linear Algebra

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Homework is due in class and must be stapled, with your name on it, to receive credit.

You may find the Mathematics Help Room (MATH 175) to be useful in obtaining extra assistance with your homework.

You may find it useful to use a computer algebra system to help with matrix operations.
The progam Mathematica is available free to students via the University of Colorado.

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Date	Topics covered	Reading	Homework Assignments
Monday January 14	Class introduction, review.	Review class notes
Wednesday January 16	Definition of a vector space, examples of vector spaces, sub-vector spaces.	Review class notes
Friday January 18	Linear maps, images, kernels.	Read 2.1	HW1: Due Friday January 25 Problems A-F .pdf
Monday January 21	NO CLASS	NO CLASS	NO CLASS
Wednesday January 23	Sec 2.1 Matrix multiplication.	Read 1.1
Friday January 25	Sec 1.1 Systems of linear equations.	Read 1.2	HW 2: Due Friday January 31 Problems G-L .pdf Sec 2.1: 1-12, 31, 32, Sec 1.1: 1-6, 11-14.
Monday January 28	Sec 1.2 Row reduction and echelon form.	Read 1.3-4
Wednesday January 30	Sec 1.3-4 Vector equations, the matrix equation Ax=b.	Read 1.5
Friday January 31	Sec 1.5 Solution sets of linear systems.	Read 1.6-7	HW 3: Due Friday February 8 Sec 1.2: 2-14 even. Sec 1.3: 2-8 even, 28, 32. Sec 1.4: 2-20 even.
Monday February 4	Sec 1.7 Linear independence.	Read 1.8-9
Wednesday February 6	Sec 1.8-9 (Re)Introduction to linear transformations (linear maps), the matrix of a linear transformation.	Read 1.10
Friday February 8	Sec 1.10 Linear models in business, science and engineering.	Review	HW 4: Due Friday February 15 Sec 1.5: 2-12 even, 18. Sec 1.6: 1, 8, 12 Sec 1.7: 2, 6, 10, 18
Monday February 11	Homework review	Review
Wednesday February 13	Review	Review	Sample Midterm I .pdf
Friday February 15	MIDTERM I 6-7 PM ECCR 200 (Extra time exams start at 5:30 PM in MATH 220)	Read 2.1-2	HW 5: Due Friday February 22 Sec 1.8: 2-24 even. Sec 1.9: 2-22 even. Sec 1.10: 1, 2, 8, 9, 10.
Monday February 18	Sec 2.1-2 Matrix operations, the inverse of a matrix.	Read 2.3
Wednesday February 20	Sec 2.3 Characterizations of invertible matrices.	Read 2.4-5
Friday February 22	Sec 2.4-5 Partitioned matrices and matrix factorizations.	Read 2.6	HW 6: Due Friday March 1 Sec 2.2: 2-28 even. Sec 2.3: 2, 5, 6, 11, 12, 14, 24, 39. Sec 2.4: 2-12 even.
Monday February 25	Sec 2.6 The Leontief input-output model.	Read 2.7
Wednesday February 27	Sec 2.7 Applications to computer graphics.	Read 2.8-9
Friday March 1	Sec 2.8-9 Subspaces of finite dimensional real vector spaces.	Read 3.1	HW 7: Due Friday March 8 Sec 2.5: 2-16 even. Sec 2.6: 2-8 even. Sec 2.7: 2-16 even. Sec 2.8: 1-6, 15-20.
Monday March 4	Sec 3.1 Introduction to determinants.	Read 3.2
Wednesday March 6	Sec 3.2 Properties of determinants.	Read 3.3
Friday March 8	Sec 3.3 Cramer's Rule.	Read 4.1	HW 8: Due Friday March 15 Sec 2.9: 2, 4, 6, 14, 16, 18, 20 Sec 3.1: 2, 8, 10, 20, 26, 37, 38 Sec 3.2: 6, 10, 18, 21, 24, 29, 31, 32, 34, 35
Monday March 11	Sec 4.1 Vector spaces and sub-vector spaces.	Read 4.2
Wednesday March 13	Sec 4.2 Null spaces, column spaces and linear transformations.	Read 4.3
Friday March 15	Sec 4.3 Linearly independent sets, bases.	Review	HW 9: Due Friday March 22 Sec 3.3: 6, 10, 12, 18, 22, 30 Sec 4.1: 1, 2, 6, 10, 26 Sec 4.2: 2, 4, 8, 12, 16 (The following problems are recommended, but do not turn them in: Sec 4.1 28, 32, 33 and Sec 4.2 26, 28, 30, 33, 34)
Monday March 18	Homework review	Review
Wednesday March 20	Review	Review	Sample Midterm II .pdf
Friday March 22	MIDTERM II 6-7 PM ECCR 200 (Extra time exams start at 5:30 PM in MATH 220)	Read 4.4	HW 10: Due Friday April 5 Sec 4.3: 2, 4, 10, 11, 16, 22 Sec 4.4: 2, 4, 17, 18 (The following problems are recommended, but do not turn them in: Sec 4.3 24, 26, 31 and Sec 4.4 27)
Week of March 25-March 29	SPRING BREAK	SPRING BREAK	SPRING BREAK
Monday April 1	Sec 4.4 Coordinate systems.	Read 4.5
Wednesday April 3	Sec 4.5 The dimension of a vector space.	Read 4.6
Friday April 5	Sec 4.6 Rank.	Read 4.7	HW 11: Due Friday April 12 Sec 4.5: 4, 6, 14, 21 Sec 4.6: 1, 4, 10, 13, 15, 17 Sec 4.7: 1, 3, 7-10 (notes and solutions to a few problems on change of basis .pdf) (The following problems are recommended, but do not turn them in: Sec 4.5 22, 25, 29, 30 and Sec 4.6 20, 24, 27)
Monday April 8	Sec 4.7 Change of basis.	Read 4.8-9
Wednesday April 10	Sec 4.8-9 Applications to difference equations and Markov chains.	Read 5.1
Friday April 12	Sec 5.1 Eigenvectors and eigenvalues.	Read 5.2	HW 12: Due Friday April 19 Sec 4.9: 1, 4, 10, 19 Sec 5.1: 2, 6, 12, 16, 20 (The following problems are recommended, but do not turn them in: Sec 4.8 2, 4, 6, 8, 10, 19, 20, 21 and Sec 5.1 22, 23, 25, 26, 27, 30)
Monday April 15	Sec 5.2 The characteristic equation.	Read 5.3
Wednesday April 17	Sec 5.3 Diagonalization.	Read 6.1
Friday April 19	Sec 6.1 Inner product, length and orthogonality.	Read 6.2-3	HW 13: Due Friday April 26 Sec 5.3: 2, 6, 14, 22 Sec 6.1: 2, 4, 16, 19, 20 Sec 6.2: 4, 6, 11, 12, 17, 18 (The following problems are recommended, but do not turn them in: Sec 5.3 27, 31, 32, Sec 6.1 24, 28, 30 and Sec 6.2 25, 28)
Monday April 22	Sec 6.2-3 Orthogonal sets and orthogonal projections.	Read 6.4
Wednesday April 24	Further topics	Review
Friday April 26	Further topics	Review	HW 14: Due Friday May 3 Sec 6.3: 2, 6, 8, 14, 22
Monday April 29	Further topics	Review
Wednesday May 1	Homework review	Review
Friday May 3	Review	Review	Sample Final .pdf
Monday May 6	FINAL EXAM SEC 003 7:30-10:00 PM FLMG 102 (Lecture Room) Extra time starts at 7:00 PM in MATH 220	FINAL EXAM	FINAL EXAM 003
Thursday May 9	FINAL EXAM SEC 001 7:30-10:00 AM MUEN E417 (Lecture Room) Extra time starts at 7:00 AM in MATH 220	FINAL EXAM	FINAL EXAM 001

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You may find it useful to use a computer algebra system to help with matrix operations. The progam Mathematica is available free to students via the University of Colorado.

For those of you typing up your homework, you may want to consider learning to use LaTex. If you have a mac, one possible easy way to get started is with texshop. If you are using linux, there are a number of other possible ways to go, using emacs, ghostview, etc. If you are using windows, you're on your own, but I'm sure there's something online. Here is a sample homework file to use: (the .tex file, the .bib file, and the .pdf file). It is probably easiest to just look at the .tex file, and start to experiment. There is also the (Not so) short introduction to latex, which will answer most of your questions (although typing your question into your favorite search engine will probably work well, too). You may also want to try http://scribtex.com/ for a cloud version.