MATH 1107E [0.5 Credit] Linear Algebra I - Carleton …

1 MATH 1107E [ Credit] Linear Algebra I Basic Information: Class Schedule: Tuesdays and Thursdays: 18:05-19:25 starting September 5, 2013. Tutorial Schedule: Thursdays: 19:35-20:25 starting September 12, 2013. Course Instructor: Kyle Harvey Email: Office Hours: Tuesdays and Thursdays: 14:30-17:30, or by appointment. 5281 Herzberg Building Course Webpage: All course material will be made available through cuLearn. Course Information: Prerequisites: Ontario Grade 12 Mathematics: Advanced Functions, or MATH 0005 Textbook: Linear Algebra A Free Text by Jim Hefferon. The textbook can be downloaded for free from . Head to the Here Is Linear Algebra section and download by pressing the link Linear Algebra . There are also answers to exercise to help you see where you may be making errors. Course Overview: Systems of Linear equations; vector space of n-tuples, subspaces and bases; matrix transformations, kernel, range; matrix Algebra and determinants.

2 Dot product. Complex numbers (including de Moivre's Theorem, and n-th roots). Eigenvalues, diagonalization and applications. Classes All lectures will have Powerpoint Presentations posted on cuLearn. It is highly recommended that you print the slides and bring them in as we will be discussing all of the content presented in the slides. Remember, it is crucial for your learning to understand the material as well as practice the material. Keeping up with the homework assignments will be key to your success in this course. Calculators: No calculators or other memorandum will be permitted on the tests or exams. Tutorial Centre: 1160 HP (tunnel junction between Herzberg and Steacie): This is a drop-in centre where students in elementary courses can get one-on-one help in mathematics and statistics, on a first come first serve" basis. For more information, including hours of operation, see Assessment: Tutorials (10%): Tutorials is a time to practice the material.

3 You will be working in teams of 3-4 students in the tutorial practicing problems that will be given to you. You should be practicing the recommended problem sets at home, and working with you TA and fellow classmates in tutorial to make sure you are comfortable with the concepts. Practice makes perfect! To obtain your mark for the tutorial, you must answer at least 2 of the 4 questions correctly. Only the final answer will count, so make sure to check your work. Full solutions will be provided to you so that you may determine your errors (if any are made). Tutorial Tests (30%): There will be 3 tests to be taken place in the tutorials. Provided that you maintain at least 30% on every test, the lowest test will be dropped. Each test will be weighted equally. There will be no make up tests. If you provide adequate documentation (doctor s note, ), then I will adjust the weight of each test accordingly, otherwise a mark of 0 will be given for the test.

4 You must bring your student card to each test and exam and place it on your desk where it is visible. The dates of the tests will be: Oct 3, Oct 24, & Nov 21. Any request to review your grade for your test or tutorial must be done within two weeks of receiving the grade. Final Exam (60%): The final exam will be a three hour closed book exam to be held during the exam period set by Carleton University. The questions will be similar to those seen on the tests, and in the homework assignments. Students who wish to review their final examination paper must do so within two weeks from the release of final grades. This privilege is for educational purposes and not an opportunity to argue about the marking. Note: The above grading scheme applies only when the Term Grade is at least 16/40. A Term Grade of less than 16/40 will result in an automatic failure with the final grade of FND, regardless of the Final Examination.

5 Students who obtain a Term Grade of at least 16/40, but miss the Final Examination may be eligible for a deferred exam. Application for a deferral must be made, with appropriate documentation, to the Registrar's Office within five working days after the examination. Please note that the deferred exam for this course will be the final exam for the Winter term course and will be written in April. In addition, you must achieve at least a 40% on your final exam and 50% overall to pass this course. Policies: Academic Integrity: All tests and exams are to be done independently. Any instance of suspected cheating or plagiarism will not be tolerated. Suspected cheating will be reported to the Dean, according to the policies stated in General Regulations. For more information, please consult: Pregnancy or Religious Write to me with any requests for academic accommodation during Obligation: the first two weeks of class, or as soon as possible after the need for accommodation is known to exist.

6 For more details see Academic Accommodations for Students with Disabilities: The Paul Menton Centre for Students with Disabilities (PMC) provides services to students with Learning Disabilities (LD), psychiatric/mental health disabilities, Attention Deficit Hyperactivity Disorder (ADHD), Autism Spectrum Disorders (ASD), chronic medical conditions, and impairments in mobility, hearing, and vision. If you have a disability requiring academic accommodations in this course, please contact PMC at 613-520-6608 or for a formal evaluation. If you are already registered with the PMC, contact your PMC coordinator to send me your Letter of Accommodation at the beginning of the term, and no later than two weeks before the first in-class scheduled test or exam requiring accommodation (if applicable). After requesting accommodation from PMC, meet with me to ensure accommodation arrangements are made. Please consult the PMC website for the deadline to request accommodations for the formally-scheduled exam.

7 Course Schedule: (Please note that course material is subject to change based on the progression of the course) Week 0 Sept 5 Course Syllabus How should I prepare for this math course? Systems of Linear Equations and Elimination Week 1 - Sept 10 & Sept 12 The 3 Types of Solutions to Systems of Linear Equations Matrix and Vector Notation Elementary Row Operations & Reduced Row Echelon Form Week 2 - Sept 17 & Sept 19 Identity Matrices & Nonsingular Matrix Matrix/Vector Operations: Addition, Scalar Multiplication and Transpose Matrix/Vector Operations: Multiplication Week 3 - Sept 24 & Sept 26 Solving Systems of Linear Equations using Matrices & Vectors Homogenous Systems & The Particular Solution Inverse of a Matrix Week 4 - Oct 1 & Oct 3 Solving using Inverse Matrices Linear Combinations of Vectors, Spans & Spanning Sets Linear Dependence & Linear Independence Test #1 to be held in tutorial (covering material from weeks 1-3) Week 5 - Oct 8 & Oct 10 Creating Linearly Independent Sets from Linearly Dependent Sets Vector Spaces & Subspaces of of n-tuples Basis for the Column Space of a Matrix Week 6 - Oct 15 & Oct 17 Basis for the Row Space of a Matrix Matrix Transformations Range of Matrix Transformations Week 7 - Oct 22 & Oct 24 Basis for the Null Space of a Matrix Dimension, Rank, and Nullity Rank Nullity Theorem Test #2 to be held in tutorial (covering material from weeks 4-6) Week Fall Break - Oct 29 & Oct 31 FALL BREAK.

8 NO CLASSES Week 8 - Nov 5 & Nov 7 Goldilocks Theorem Direct Sums Determinants Week 9 - Nov 12 & Nov 14 Elementary Matrices Properties of Determinants Eigenvectors & Eigenvalues Week 10 - Nov 19 & Nov 21 Finding Eigenvalues & Eigenvectors Similar Matrices Diagonalization Test #3 to be held in tutorial (covering material from weeks 7-9) Week 11 - Nov 26 & Nov 28 Applications of Diagonalization Complex Numbers Adjoint Matrices Week 12 Dec 3 & Dec 5 Inner Products Normal Vectors & Orthogonal Vectors