MATH 3130.001 Introduction to Linear Algebra
Fall, 2015
Meetings: 1:40 am - 2:55 pm, Tu,Th, ENGR 107
Instructor: Greg Morrow
Office: ENGR 284, (719) 255-3184, gmorrow@uccs.edu
Hours: Tu, Th 11:00 - 11:30 am, and 3:30-4:30 pm, or by appointment.
Prerequisite: Calculus III (MATH 2350)
Text: Elementary Linear Algebra, 11th ed., by Howard Anton (2014), John Wiley & Sons: Hoboken, NJ. ISBN:
978-1-118-47350-4
Description: Linear algebra is a fundamental tool for solving applied mathematics problems involving several
variables. There are both computational and conceptual sides to this subject. At first the hand-computational
side will be stressed to lay a groundwork for the concepts. Later more emphasis will be placed on the conceptual
sequence of operations. On the conceptual side we will see many theorems. The theory can provide a general
perspective, likened to the view from a mountaintop over a valley of applications. Some problems involving the
words show or prove will be assigned in the homework and may occasionally be found on tests. The course
covers systems of linear equations, determinants, Euclidean vector spaces, general vector spaces, change of
basis, rank theorem, matrix transformation of Euclidean space, eigenvalues and eigenvectors, diagonalization,
inner product spaces, best approximation, least squares fitting to data, orthogonal diagonalization, quadratic
forms, and the principal axes theorem.
Homework and Tests: Homework will be collected according to the attached schedule. There will be two midsemester tests, as well as a final exam. The final exam will test primarily the material covered after the second
midterm exam. Calculators will not be allowed on tests. Homework will count 16% of the course grade, each
mid-semester test will count 27%, and the final exam will count 30%. There will be no make-up for late
homework. Arrangements for make-up exams must be made in advance except in extraordinary circumstances.
Also, in the event that a make-up exam is approved, the student is responsible to make an appointment with the
testing center, dservice@uccs.edu
Final Exam: Tuesday, Dec. 15, 12:40 pm - 2:40 pm.
Grading. 90 => grade of A, 80 => B or better, 70 => C or better. Half grades (e.g. B+) are possible.
Peer Assisted Study Sessions (PASS): A Peer Assisted learning component is provided for all students who
want to improve their understanding of the material taught in this course. Study sessions are led by a student
who has already mastered the course material and has been trained to facilitate group sessions where students
can meet to compare class notes, review and discuss important concepts, develop strategies for studying, and
prepare for exams. Attendance at these sessions is free and voluntary. Students may attend as many times as
they choose. The sessions begin the first week of class and continue throughout the semester. A session
schedule will be announced in class and may be found on the Math Center website
http://www.uccs.edu/mathcenter/peer-assisted-study-sessions.html
MATH 3130.001 Introduction to Linear Algebra Fall, 2015
Syllabus (subject to change: revised Aug. 10, 2015)
Date
Coverage in Text DUE DATES
8/25-8/27
1.1-1.4.
9/1-9/3
1.5-1.7.
HW I due 9/3
9/8 Labor day holiday observed, no class
9/10
2.1-2.3.
HW II due 9/10
9/15-9/17 3.1-3.5.
HW III due 9/17
9/22-9/24 4.1- 4.3.
HW IV due 9/24
9/29-10/1 review for test; Test 1 on Ch. 1-3 on 10/1.
See Added Instructions for HW V.
10/6-10/8
4.4- 4.5.
10/13-10/15 4.6-4.8.
HW V due 10/8
HW VI due 10/15
10/20-10/22 1.8 (not a typo), 4.9, 4.10. HW VII due 10/22
10/27-1029
11/3-11/5
11/10-11/12
5.1-5.2.
review for test
6.1-6.3.
11/17-11/19 6.4-6.5;
11/24
HW VIII due 10/29
Test 2 on Ch. 4 on 11/5.
HW IX due 11/12
HW X due 11/19
7.1;
Thanksgiving holiday 11/26.
12/1-12/3
7.2-7.3;
HW XI due 12/1
12/8-12/10 review for final exam. HW XII due 12/8
12/15 Final Exam, 12:40-2:40 pm, covers Ch. 5, 6, 7.
MATH 3130.001 Introduction to Linear Algebra Fall, 2015
Homework (HW). (EC = extra credit)
HW I.
1.1: 6, 8, 10c, 14, 16, 20a, 26; 1.2: 2, 3a,c,d, 5, 9, 19, 27; 1.3: 5d,j, 7, 10, 12, 21; 1.4: 3b, 5, 10, 15, 28.
HW II.
1.5: 4c,d, 6b, 8, 9, 15; 1.6: 7, 12, 15, 17; 1.7: 14, 16, 22, 26, 32, 35, 40a.
HW III.
2.1: 1, 6, 8, 15, 18, 19a,d,f, 23, 32; 2.2: 3, 7, 9, 11, 19, 21, 23, 26, 27, 29; 2.3: 3, 5, 12, 19, 24.
HW IV.
3.1: 13, 20, 23; 3.2: 12, 18, 24; 3.3: 8, 12, 13, 18, 28, 36; 3.4: 6, 15, 17, 21, 23; 3.5: 8, 9, 17, 32.
HW V.
4.1: 4, 5, 6, 7, 10; 4.2: 1, 3, 8, 12, 15a,c; 4.3: 2, 8, 10, 11, 15, 23(EC).
Added Instructions for HW V. Section 4.1: 4, 5, 6, 7, 10: The structures of problems 4.1 #5 and #7
are NOT vector spaces--show a specific EXAMPLE for each axiom that does not hold in these cases;
see answers in back of book for axioms that do not hold for these problems. The spaces in problems
4.1 #4, #6, and #10 are subsets of known vector spaces that happen to satisfy the closure axioms
(namely, axioms 1 and 6) --- in these problems verify ONLY axioms 1 and 6 --- skip verification of the
other axioms. Section 4.2: 1, 3. In problems 4.2 # 1a,c,e and 4.2 #3a,b,d verify that the given sets
ARE vector subspaces by verifying both (closure) conditions of Thm. 4.2.1. On the other hand, in
problems 4.2 # 1b,d and 4.2 #3c provide an EXAMPLE to show that one of the closure conditions of
Thm. 4.2.1 does not hold for the given set of vectors. Thus verify that the given sets in these problems
ARE NOT vector subspaces.
HW VI.
4.4: 2, 4, 8, 12, 14, 17, 23a,b. 4.5: 6, 7, 8, 12, 14(EC), 16.
HW VII.
4.6: 1, 8, 10, 12(EC); 4.7: 4, 6, 10a, 13, 17, 20(EC). 4.8: 4, 6, 9, 18, 19, 20, 25.
HW VIII.
1.8: 11a, 12b, 14c, 15, 24a, 31b; 4.9: 2, 4, 6, 9,11a, 22, 25, 27; 4.10: 1, 5, 8a, 9a, 11, 17, 19, 23.
MATH 3130.001 Introduction to Linear Algebra Fall, 2015
HW IX.
5.1: 2, 7, 10, 12, 20, 23, 25; 5.2: 2, 4, 8, 10, 13, 18, 27.
HW X.
6.1: 8, 17, 23, 28, 32, 38 (EC). 6.2: 4, 16, 18, 19, 21, 25, 29; 6.3: 10, 15, 19, 29, 34, 37.
HW XI.
6.4: 1, 2, 3, 7, 11, 16, 17, 25, 27; 6.5: 1, 2, 3, 5. 6.3: 43(EC); 6.6: 4(EC).
HW XII.
7.1: 4a, 6, 8, 13 23; 7.2: 4, 6, 9, 12, 18, 19, 26(EC).
Extra Credit HW:
7.3: 2, 4, 5, 6, 14, 21, 25. DUE: 12/15, 12:40 pm.
Math Center
The Math Center is a study space for all students on campus, whether you need a little help, a lot of help, or
none at all. They have a staff of about 20 tutors that have taken at least through Calculus 3 (although many of
them have taken several math classes beyond Calculus 3), and who have been trained to work with students one
on one. The center is a great place to sit on your own or with classmates, work on homework, study for exams,
review concepts from previous classes, or just check your homework answers. The Math Center is located in
Engineering 233. Come in, sign in, and have a seat. If you have a question, raise your hand and a tutor will come
to you. You can find the schedule of tutors, and a lot more information about the center
at http://www.uccs.edu/mathcenter