MAT 202 Linear Algebra
MTWR 7:30-9:20, Summer 2017 6/12-8/06
Betsy McCall, M.A., M.S.,
Assistant Professor of Mathematics
Anne Arundel Community College /
(410) 777-1264
Mathematics 231J
Office Hours / MW 6:30-7:30, TR 7-7:30
Or by appointment
Course Websites / Canvas Course
Archive Site betsymccall.infoor
Course Description / Study linear transformations on finite-dimensional vector spaces. Topics include linear systems, matrices, determinants, inner product spaces, and eigenvalues.
Prerequisite: MAT 191
Learning Objectives / At the conclusion of this course, students will be able to:
- Solve systems of linear equations using a variety of matrix algebra techniques.
- Use the properties of matrix operations, inverses, and determinants to solve matrix algebra problems.
- Find the dimension and bases for a variety of vector spaces and subspaces.
- Use the properties of inner product spaces to create an orthonormal basis, find the angle between vectors, and check for orthogonality.
- Analyze the properties of transformations in function notation, prove linearity or nonlinearity, and write its matrix representation.
- Find and apply the eigenvalues and eigenvectors of a linear transformation.
- Prove basic theorems of linear algebra.
- Apply the techniques of linear algebra to solve problems from the physical and social sciences.
Required Materials / Textbook: “Elementary Linear Algebra”, 7th Edition (2013), Ron Larson, Brooks/Cole.
Software: We will also be using MatLab for out-of-class lab assignments. These programs are available in the Math computer labs, and you can access them from home through Citrix.
Calculator: It is strongly recommended that students obtain a TI-83/84 calculator. Students may not use a TI emulator on their smartphones or tablets during exams. Students may also not use any CAS calculators such as the TI-89/92 during any in-class assessments.
Attendance / Attendance is class is required of all students. We will be doing a number of in-class group activities, some of which will be extremely difficult to replicate by oneself outside of class. AACC faculty are required to report attendance daily. If you must miss class, you can submit assignments to me by email before the end of class (scan or take a clear photo). Late assignments will be assessed a 50% penalty. Exceptions to this policy will be made only under extreme circumstances, or if arrangements are made in advance of the absence.
Grading / Midterm Exams (x3) – 100 points each (300 points total)
Final Exam – 200 points
Written Homework – 125 points
Proof Sets – 100 points
Computer Assignments/Labs – 100 points
Modeling Project – 50 points
Quizzes – 125 points
The total course grade is out of 1000 points. Grades will be awarded as follows:
F: 0-599 points
D: 600-699 points
C: 700-799 points
B: 800-899 points
A: 900+ points
Exams / Exams will be given in class. Make-ups will be allowed if 1) prior permission is obtained and make-up time is scheduled in advance (more than 48 hours!), 2) under exceptional circumstances. Students are responsible for contacting me in a timely fashion. Once a graded exam is returned to students, the exam cannot be made up under any circumstances.
Final Exam: Thursday, August 3, 2016, 7:30-9:30 p.m.
The final exam is comprehensive, but will emphasize more recent material.
Attendance, Participation and Written Homework / As noted above, faculty are required to report attendance to the college daily. You must attend 75% or more of classes to be consider “attending” for reporting purposes. Excessive absences may result in penalties of 3 points per missed day. As the summer will go extremely fast, missing class time is to be avoided if possible.
We will be doing a number of in-class activities to accompany learning in the classroom, some of which are noted on the syllabus. Students who fail to participate in these activities will lose participation points.
Written homework points will be added on top of this, so you may be able to submit additional assignments to make up for missed participation points.
Projects / Students will be completing a number of projects during the course of the semester. One project will be completed in class working in groups (50 points). There will be a number of short MatLab projects (10 points each) roughly once per week. More information on these projects will be forthcoming. Labs will be completed outside class, generally speaking, although we may meet in a computer lab from time to time to sort out “bugs”, as noted in the syllabus. Students may use any of the open math labs such as MATH 206 or CRSC 190 if you don’t have the required software at home. There will be a final project that students can choose to do from among several topics.
Quizzes / In general there will be at least one short in-class quiz per week, each one worth 12-15 points. There are intended to give you some idea of the kinds of questions to expect on forthcoming exams, and to give you some idea of how I might ask questions different from/similar to the textbook. While more than 100 points will be theoretically available to account for missed quizzes, no more than 100 points may count toward the final course grade. Missed quizzes cannot be made up.
Tutoring / Help with the material is available during my posted office hours, by appointment, or by email. You may also visit the Math Lab in Library 102 for additional assistance (subject to the availability of tutors). It is recommended that you seek out help early and often rather than wait until you are in a hole difficult to climb out of.
Special Needs / Notice of Nondiscrimination: AACC is an equal opportunity, affirmative action, Title IX, ADA Title 504 compliant institution. Call Disability Support Services, 410-777-2306 or Maryland Relay 711, 72 hours in advance to request most accommodations. Requests for sign language interpreters, alternative format books or assistive technology require 30 days’ notice. For information on AACC’s compliance and complaints concerning sexual assault, sexual misconduct, discrimination or harassment, contact the federal compliance officer and Title IX coordinator at 410-777-1239, or Maryland Relay 711.
The Disability Support Services Office is located in SSVC room 200 (Student Services Building).Appropriate and reasonable academic accommodations will be provided to all qualified individuals. Confirmation of disability will be required. For further information, refer to the College Catalog.
Note that accommodations granted in the middle of the semester will not go into effect retroactively, so it is important to go through the proper channels as early as possible.
Technology in the Classroom / Please turn off all cell phones and other electronic devices while in class. Use of these items is strictly forbidden during tests. If you wish to use a tablet or laptop for note-taking, you may ask permission to do so, but do not abuse the privilege by listening to music, watching videos, checking Facebook, or other non-class-related activities while class is going on. It is distracting to other students, and I will rescind permission to use your device in class if a student cannot stay on task.
Calculators on phones and tablets are okay to use during in-class activities and for homework, however, they will not be permitted during in-class quizzes or during tests. Do not count on me having a spare for you to borrow.
Weather Policy / If the college is officially closed for any reason, the activities and material scheduled for the day on which the college was closed will be covered / take place during the next class meeting. This includes scheduled tests. Unless otherwise announced online homework due dates will still be in effect as officially scheduled. Sign up for emergency alert text messages at .
Academic Integrity / Academic honesty is expected at all times from all AACC students. There is never a reason to cheat, facilitate, plagiarize or otherwise not show integrity. Behavior violating the school’s Academic Integrity Policy will result in severe sanctions. They can range from zero points for the respective assignment/quiz/test to a failing class grade, and do not have to be limited to sanctions involving grades. Other sanctions, e. g. community service, can be imposed as well. If this is a repeat or even more severe offense, harsher penalties than failing the class may be given. Each violation of the Academic Integrity Policy will be formally put in an incident report and forwarded to the appropriate college representative. The complete academic integrity policy can be found in the online College Catalog – College Policies and Procedures – Academic Integrity Policy.
Student Opinion Forms / Toward the end of the semester you will be asked to fill out an online Student Opinion Form to provide feedback on your learning and your instructor’s teaching concerning this course. Your responses will be anonymous and your instructor will receive the results only after submitting final grades. Your input is important because it may offer information, recommendations, or ideas to improve teaching and learning at AACC. You can be assured that all comments will be read and taken into consideration to make this class the best it can be. Please follow the request to participate.
If 80% of the class completes the opinion survey, everyone will get 5 bonus points.
The Greek alphabet
Letter name / Uppercase / Lowercase / Letter name / Uppercase / Lowercase
Alpha / / / Nu / /
Beta / / / Xi / /
Gamma / / / Omicron / /
Delta / / / Pi / /
Epsilon / / / Rho / /
Zeta / / / Sigma / /
Eta / / / Tau / /
Theta / / / Upsilon / /
Iota / / / Phi / /
Kappa / / / Chi / /
Lambda / / / Psi / /
Mu / / / Omega / /
Tentative Schedule
Week / Dates / Topics/Sections Covered / Comments/Due Dates
1 / 6.12 / Introduction to the Course
1.1 Introduction to Systems of Linear Equations, 1.2 Gaussian Elimination and Gauss-Jordan Elimination
6.13 / 1.3 Applications of Systems of Linear Equations, 2.1 Matrix Operations / Quiz #1
6.14 / 2.2 Properties of Matrix Operations, 2.3 Inverse of a Matrix / Sections 1.1-1.3, 2.1 (Homework #1)
Quiz #2
6.15 / 2.4 Elementary Matrices, 2.5 Applications of Matrix Operations / Lab #1
Quiz #3
2 / 6.19 / Review for Exam #1 / Sections 2.2-2.5 (Homework #2)
Quiz #4
6.20 / Exam #1 covers Chapters 1, 2
6.21 / 3.1 Determinant of a Matrix, 3.2 Evaluation of a Determinant using Elementary Matrix Operations / Proof Set #1
6.22 / 3.3 Properties of Determinants, 3.4 Applications of Determinants / Lab #2
Quiz #5
3 / 6.26 / 4.1 Vectors in Rn,
4.2 Vector Spaces / Sections 3.1-3.4
(Homework #3)
Quiz #6
6.27 / 4.3 Subspaces of Vectors Spaces / Quiz #7
6.28 / 4.4 Spanning Sets and Linear Independence, 4.5 Basis and Dimension / Sections 4.1-4.3
(Homework #4)
Quiz #8
6.29 / 4.6 Rank of a Matrix and Systems of Linear Equations, 4.7 Coordinates and Change of Basis
Review for Exam #2 / Quiz #9
4 / 7.3 / No class, Independence Day holiday / Quiz #10 (due online)
7.4 / No class, Independence Day
7.5 / Exam #2 covers Chapter 3, 4 / Section 4.4-4.7
(Homework #5)
Lab #3
7.6 / 5.1 Length and Dot Product in Rn,
5.2 Inner Product Spaces / Proof Set #2
5 / 7.10 / 5.3 Orthonormal Bases: Gram-Schmidt Process, 5.4 Projections / Section 5.1, 5.2
(Homework #6)
Quiz #11
7.11 / 6.1 Introduction to Linear Transformations, 6.2 Kernel and Range of a Linear Transformation / Lab #4
Quiz #12
7.12 / 6.3 Matrices for Linear Transformations, 6.4 Transition Matrices and Similarity / Sections 5.3, 6.1-6.2
(Homework #7)
Quiz #13
7.13 / 6.5 Applications of Linear Transformations / Quiz #14
6 / 7.17 / Review for Exam #3 / Sections 6.3-6.5
(Homework #8)
Quiz #15
7.18 / Exam #3 covers Chapters 5, 6 / Lab #5
7.19 / 7.1 Eigenvalues and Eigenvectors / Proof Set #3
7.20 / 7.2 Diagonalization / Quiz #16
7 / 7.24 / 7.3 Symmetric Matrices and Orthogonal Diagonalization / Lab #6
Quiz #17
7.25 / 7.4 Applications of Eigenvalues and Eigenvectors, Discrete Dynamical Systems, Markov Chains / Sections 7.1. 7.2
(Homework #9)
Quiz #18
7.26 / 7.4 Exponential of a Matrix
Systems of Linear Differential Equations / Quiz #19
7.27 / 5.4 Projections & Regression
Regressions Project / Proof Set #4
Sections 7.3, 7.4 (Homework #10)
Quiz #20
8 / 7.31 / Regressions Project / Lab #7
8.1 / Regressions Project / 5.4
(Homework #11)
8.2 / Review for Final Exam
8.3 / Final Exam: Thursday, August 3rd, 2016, 7:30-9:30 p.m. / Comprehensive, emphasizes applications
Final deadline for make-up/bonus homework/labs 8.03