MA122 syllabus PDF

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MA122 syllabus...

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Fall Term, 2017

MATHEMATICS 122 - Introductory Linear Algebra Lectures MA122A TTh 8:30am-9:50am in LH1010 – Dr. Sohail MA122B TTh 1:00pm-2:20pm in BA101 – Dr. Weatherby MA122C TTh 4:00pm-5:20pm in LH1010 – Dr. Zhang Instructors/Lab Coordinator Dr. Nasir Sohail Office: LH3064 Phone: x4900 Email: [email protected] Office Hours Wed 12pm - 1:30pm, Fri 12pm - 1:30pm (or e-mail for appt.) Dr. Chester Weatherby Office: LH3043 Phone: x4142 Email: [email protected] Office Hours Mon 4pm - 5pm, Tues 4pm - 5pm, Fri 3:30pm - 4:30pm (or e-mail for appt.) Dr. Ping Zhang Office: LH3065 Phone: x4902 Email: [email protected] Office Hours Tues 2pm - 3pm, Wed 10am - 11am, Thurs 2pm - 3pm (or e-mail for appt.) Trevor Saunderson Lab Coordinator

Office: LH3048

Phone: x3012

Email: [email protected]

Relation to Other Courses: MA122 is the prerequisite for MA201 Multivariable Calculus, MA222 Linear Algebra, MA270 Financial Math I, MA305 Differential Equations II, MA307 Numerical Analysis, MA343 Introduction to Multivariate Analysis, ST230 Introduction to Probability and Statistics for Science, ST259 Probability I and ST362 Regression Analysis. Some of these courses in turn provide prerequisites for higher level courses in mathematics and statistics. Textbook: Daniel Norman & Dan Wolczuk, Introduction to Linear Algebra for Science and Engineering, 2nd edition, Pearson, 2012. Calculators: Students may only use the approved scientific calculator, Casio FX-300MS Plus, on course tests and the final examination. No other calculator is allowed. MyLearningSpace: (https://mylearningspace.wlu.ca/) Course materials are available on MyLearningSpace, and any new/supplemental materials will be posted online as well. You should check the MA122 page regularly. Note, do not use the MyLearningSpace email system for this course. Tentative Schedule of Topics (references are to the textbook ): Week 1 2 3 4 5 6 7 8 9 10 11 12

Topics Vectors, lines, addition and scalar multiplication in R2 and R3 Rn , subspaces, spanning sets, linear independence and basis, Length and dot product, equations for planes Projections, orthogonal projections, minimum distance, cross-product and volume Systems of linear equations, matrix methods, row echelon form Reduced row echelon form, rank of a matrix, homogeneous systems Spanning and linear independence problems, bases of subspaces Matrix addition, scalar multiplication of matrices, and matrix multiplication Matrix and linear mappings, geometric transformations, Special subspaces for linear systems and linear mappings, rank theorem Inverse matrices and mappings Elementary matrices, the determinant of a matrix and properties Matrix inverse by cofactors, Cramer’s rule, connections area/volume Eigenvalues/eigenvectors, characteristic polynomial, algebraic/geometric multiplicities Diagonalization of a square matrix and some applications

Section 1.1 1.2 1.3 1.4, 1.5 2.1 2.2 2.3 3.1 3.2, 3.3 3.4 3.5 3.6, 5.1, 5.2 5.3, 5.4 6.1 6.2, 6.3

Course Goals and General Learning Outcomes: Linear algebra is essentially the study of vectors, matrices and linear mappings. Since linear structure is a geometric model of natural and social phenomena using the simplest algebraic computations, linear algebra plays an extremely important role in almost every branch of natural and life sciences, social sciences, business and management as well as mathematics itself. This introductory course deals with only Euclidean real spaces. Abstract concepts are introduced with geometric intuition. General patterns of applications are summarized with algorithms or recipes. General theorems are all illustrated by concrete examples, together with proofs in a few steps or by algorithms. The aim of the course is to provide students with tools that can be applied right away in higher level mathematics courses and in other disciplines, and to prepare students for a more abstract and systematic study of linear algebra in the course MA222. At the end of the course, students are expected to be able to: • Solve geometric problems concerning lines and planes in Euclidean spaces in terms of their algebraic equations in vector and scalar forms. • Determine whether a set of vectors is linearly independent and determine whether a subset of a Euclidean space is a subspace. • Use the dot product and cross product of vectors to interpret and solve geometric problems. • Find a basis for a subspace of a Euclidean space, in particular, for the solution space of a homogeneous system of linear equations. • Solve systems of linear equations and express the general solution as a particular solution plus a solution to the corresponding homogeneous system. • Perform matrix operations and compute determinants of square matrices. • Determine whether a square matrix is invertible and, if it is, find its inverse. • Interpret and solve problems related to linear systems and linear mappings using matrices and their properties. • Find real eigenvalues of a square matrix and their corresponding eigenspaces. • Determine whether a square matrix (or a linear operator) is diagonalizable. Evaluation: A final mark out of 100 will be calculated as follows: i-Clicker Questions (participation) Weekly Online WeBWorK Homework Bi-Weekly WeBWorK Lab Quizzes Bi-Weekly Lab Assignments Midterm Test (Monday, Oct. 30th, 2017, 7:30pm - 8:50pm) Final Examination (2.5 hours, date & time to be announced)

4% 7% 7% 10% 27% 45% 100%

Note 1: To be eligible to pass this course, a student must score at least 40% on the Final Examination. Note 2: Final numeric marks will be calculated as a percentage according to the above formula and then be converted to a letter grade in accordance with the current Undergraduate Calendar. Midterm Test: The 80 minute midterm test will occur the evening of Monday October 30th, 2017 from 7:30pm - 8:50pm in various locations to be announced later. If you arrive late, no extra time will be granted. In the event of a conflict, alternative arrangements may be possible; report the conflict to your instructor at least two weeks in advance of the test. Missed Midterm Test: There will be no deferred tests. If you miss the midterm test without a valid, documented excuse (e.g., medical certificate) you will be assigned a mark of zero. The weight of a test missed for legitimate, documented reasons will be transferred to the final examination. Checking Marked Midterm Test: Your marked test papers will be returned as soon as possible, during your lab. Grades, solutions and a marking scheme for the test will be posted on MyLearningSpace (https://mylearningspace.wlu.ca/). If you find that marks have been added incorrectly or that you

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disagree with the marking of your paper, see your instructor as soon as possible. Appeals will not be accepted after two weeks of the papers being returned. i-Clickers: Throughout the semester, we will make use of i-clickers for real-time question/response polling. This classroom activity is meant to actively engage you during class time and increase your understanding of topics covered during class. The portion of your final grade coming from i-clicker questions will be solely on a participation basis, so attend class and answer clicker questions for marks. For full marks, you must participate in at least 75% of the clicker questions over the semester. Note that it is important that you attend your official registered section of MA122 in order to get participation credit. Answering clicker questions in your non-registered section will not count toward your participation grade. You are responsible for purchasing your clicker from the Laurier Bookstore. You are required to register your clicker online via MyLearningSpace (https://mylearningspace.wlu.ca). When you login, you will see a course similar to Clicker Registration – Fall 2017. To register your clicker, follow these steps: 1. Enter the Clicker Registration – Fall 2017 course by clicking on the title. 2. From the homepage, click on the Click here to register your clicker link. 3. Enter your clicker serial Remote ID in the box provided. 4. Click on the Register button. Please note: Failure to register your clicker in this way may result in loss of clicker marks. You MUST complete the registration to have your clicker marks assigned to you. If you registered your clicker in a previous term, you may not need to register again, but please CONFIRM that your clicker is registered in the registration area in MyLearningSpace. If you registered your clicker in previous years, you MUST register it again for this term. Please direct any questions about this process or about clickers in general to [email protected]. A clicker troubleshooting station is available at the help desk in the concourse (Waterloo) or in the BRAC (Brantford). Operating someone elses clicker is a serious offence (just like taking an exam for another student) and is considered Academic Misconduct. All students involved may be severely penalized. Assigned Textbook Problems: A necessary condition for succeeding in MA122 is to do assigned recommended problems from the textbook (see MyLearningSpace for the full document/list). Pay extra attention to the conceptual problems which students often find more challenging. Homework problems from the textbook will not be collected and are for your own practice and mastery of the course material. The relevant problems should be attempted immediately after the corresponding material has been covered in class, and before the weekly online WeBWorK Homework (see below). There are solutions to the Practice Problems, Chapter Review Quizzes, as well as MidSection Exercises at the back of the textbook in Appendices A and B. Non-assigned problems can be attempted for extra practice and it is a good idea, when the end of a chapter is reached in the text, to work through the Chapter Review material to test your understanding of the completed chapter. Weekly Online WeBWorK Homework: Each week you are expected to complete an online homework assignment in the WeBWorK system. The homework will be released (opened) by Monday evening of a given week, and will be due on the following Sunday at 6:00pm when the homework set will be closed and answers will become visible. The online homework is part of your lab preparation. The best 10 (of 12) weekly homework assignments will be taken to compute your homework grade. More details of this will be given during your first lab meeting, though the first homework assignment is due prior to the first lab. WeBWorK for MA122 can be found directly at: http://webwork.wlu.ca/webwork2/MA122_F17/. To login for the first time, use your user name for MyLearningSpace as the user name (i.e., the first 4 letters of your last name followed by the last 4 digits of your student number). The default password is your 9-digit student number. You should then change your password by visiting the “Password/Email link in the “Main Menu on the left side of the page. The following link will lead to a video tutorial on 3

how to use the WeBWorK system: https://www.youtube.com/watch?v=IpEozRiMXPw. Additionally, when you log in, at the top right under “Course Info”, there are links to further information on typing answers in the online system. Laboratories: There will labs every other week, starting on Monday September 18th, 2017. (If you have already missed a scheduled lab, contact your Lab Coordinator as soon as possible). Lab attendance is mandatory. Lab sessions are designed to develop mathematical skills and to investigate applications and extensions of the concepts covered in lectures, and familiarize students with the MAPLE computer package. Each lab will have two components: (1) a written lab portion followed by (2) a WeBWorK Quiz. The WeBWorK quiz will be a sampling of problems from the online WeBWorK homework that would have been due the evening prior to the lab, as well as the Sunday before that. When computing the two parts of your final lab grade, the best 5 (of 6) WeBWorK lab quizzes and the best 5 (of 6) written lab assignments will be taken. Your lab coordinator will explain this further at your first lab meeting. In all cases, validate any missed labs. Each lab session will start with a short lecture by the Lab Coordinator. A set of problems based on current work and required skill level will be handed out (the written lab component), and students will complete as much of the report as they can in the time allotted. Students can ask questions of the undergraduate instructional assistant (IA) in charge of the lab concerning general approaches to take, etc. and also discuss problems with classmates, however students must independently write their lab reports. Direct copying will be treated as academic misconduct. In preparation for each lab, students are expected to have attempted a sufficient amount of assigned homework problems pertaining the lab topics and to have worked through the lab preparation for that week. Lab preparation materials, as well as solutions to lab reports will be available through MyLearningSpace (https://mylearningspace.wlu.ca/) on the course lab page. Tips for Success and where to get help: 1. Attend class and take notes. 2. Textbook reading and exercises: Working on problems and practicing the calculations/algorithms is a basic requirement for MA122. You are expected to understand the conceptual and proof-type components of each section as we progress through the course. There will be up to 25% conceptual (including proof-type) problems on the test and exam. 3. Instructor Office Hours: If you experience difficulty with any aspect of the course, you should consult your instructor without delay. Drop by during the posted office hours, or e-mail for an appointment. 4. MyLearningSpace: You should regularly visit the MA122 page in MyLearningSpace. It contains information pertinent to the course, such as details of upcoming tests and examinations, and any other announcements about the course. 5. Math Assistance Centre: The MAC offers help for students, and provides academic support for all 100-level math course content. The MAC is open Monday to Friday and works on a drop-in basis and is located in LH1018 (Lazaridis Hall). For more information and hours of operation, see the MAC website at: http://www.wlu.ca/mac. 6. Khan Academy: A free online resource with posted videos of lessons on various topics. The lessons are prepared by individuals outside of Wilfrid Laurier University and the instructor does not ensure the material presented is correct. That said, the Khan Academy website can be a useful resource for help.

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Notes Students are expected to be aware of and abide by all University regulations and policies, as outlined in the current Academic Calendar. In particular, 1. Final Examinations Students must reserve the examination period of December 9-22, 2017. If you are considering registering for a special examination or event, you should select a time outside the examination period. Consult Academic Regulations in the Academic Calendar for special circumstances for examination deferment. 2. Special Needs Students with disabilities or special needs are advised to contact Laurier’s Accessible Learning Centre for information regarding its services and resources. Students are encouraged to review the Undergraduate Academic Calendar, https://legacy.wlu.ca/calendars/index.php?cal=1&y=73, for information regarding all services available on campus. 3. Academic Integrity/Misconduct (cheating, plagiarism) The University has a defined policy with respect to Academic Misconduct; penalties are severe and enforced at all times. You are responsible for familiarizing yourself with the academic misconduct policy and penalty guidelines, and are cautioned that, in addition to failure in a course, students may be suspended or expelled from the University for academic misconduct, and the offence may appear on their transcripts. The relevant policy can be found at Laurier’s academic integrity website along with resources to educate and support you in upholding a culture of integrity; see https://students.wlu.ca/academics/academic-integrity/index.html. Ignorance of Laurier’s academic misconduct policy is not a defence. Academic Misconduct includes transmission or reception of information, or possession of unauthorized information, during laboratories, quizzes, tests, or examinations. Academic Misconduct also includes plagiarism. Wilfrid Laurier University uses software that can check for plagiarism, and students may be required to submit their written work in electronic form for a plagiarism check. The Student Code of Conduct and Discipline and the procedures for investigating and determining appropriate disciplinary measures for breaches of this Code are given in the Academic Calendar. 4. Classroom Use of Electronic Devices The use of electronic devices in the classroom is governed by WLU Policy 9.3: Policy on the Classroom Use of Electronic Devices. Details of this Policy and the consequences of breaches are stated in the Academic Calendar. Mobile devices are permitted in this course provided they do not detract from the learning of any student, for example by noise level or by the display of distracting or disturbing content. Responsibility for enforcing this rule rests with both the instructor and the students. Students who do not feel comfortable approaching another student can email or talk to the instructor in person. Students who fail to comply with this policy may receive a verbal and/or written warning, or may be asked to leave the classroom for all or part of the course. 5. Intellectual Property The educational materials developed for this course, including, but not limited to, lecture notes and slides, handout materials, examinations and assignments, and any materials posted to MyLearningSpace, are the intellectual property of the course instructor. These materials have been developed for student use only and they are not intended for wider dissemination and/or communication outside of a given course. Posting or providing unauthorized audio, video, or textual material of lecture content to thirdparty websites violates an instructors intellectual property rights, and the Canadian Copyright Act. Recording lectures in any way is prohibited in this course unless specific permission has been granted by the instructor. Failure to follow these instructions may be in contravention of the universitys Code of Student Conduct and/or Code of Academic Conduct, and will result in appropriate penalties. Participation in this course constitutes an agreement by all parties to abide by the relevant University Policies, and to respect the intellectual property of others during and after their association with Wilfrid Laurier University.

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Course Drop Dates Fall 2017 September 13: September 20: November 8:

Last day to drop/withdraw from 12-week course(s) at no tuition charge (provided the student remains registered in at least one course). Last day to drop/withdraw from 12-week and full-year course(s) at 10% tuition charge (assessed of course rate). Last day to drop/withdraw without failure and for possible tuition adjustment (tuition charge assessed at 55% of the course rate).

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