Math 2331 (Linear Algebra), Sections 05+06, Fall 2021
| Course Information | |||||
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| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
(Sec 06) MWR 10:30pm-11:35am, Richards 155 (Sec 05) MWR 1:35pm-2:40pm, Hastings Suite 101 |
MW 3:00pm-5:00pm Online, via Zoom or by appointment in 571 Lake Hall |
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| For detailed information about the course, please consult the 2331 Course Syllabus. (Note: any information given in class or on this webpage supersedes the written syllabus.) | |||||
| Teaching Assistant | Recitation Time | Office Hours | |||
| Oleksii Sorokin sorokin.o at northeastern dot edu |
R 4:00pm-5:00pm Online, via Zoom |
T 4:30pm-6:00pm Online, via Zoom |
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| All homework assignments are available on the 2331 WeBWorK page. To log in, your username is the same as your Northeastern username, and your password is your 7-digit Northeastern ID number without the two leading zeroes. During the semester, each student has THREE individual 24-hour extensions that may be applied to any WeBWorK assignment (no reason needs to be given, simply email the instructor and request your extension). |
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| The instructor will write lecture notes for the course (see below) to supplement the official textbook as the semester progresses. The course will follow the presentation in O. Bretscher's "Linear Algebra With Applications" (5th edition), but it is NOT necessary to purchase or use the textbook for this course. | |||||
| Handouts / Lecture Notes | |||
|---|---|---|---|
| Handout | Topics | ||
| Chapter 1: Matrices and Systems of Linear Equations (20pp, v3.00, posted 9/5) | 1.1 ~ Systems of Linear Equations 1.2 ~ Matrix Operations: Addition and Multiplication 1.3 ~ Inverse Matrices and Determinants (Inverses, Determinants, Properties) |
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| Chapter 2: Vector Spaces (25pp, v3.00, posted 9/16) | 2.1 ~ Vectors in Rn 2.2 ~ The Formal Definition of a Vector Space 2.3 ~ Subspaces 2.4 ~ Linear Combinations and Span 2.5 ~ Linear Independence and Linear Dependence 2.6 ~ Bases and Dimension (Existence, Properties, Computation) |
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| Chapter 3: Linear Transformations (19pp, v3.05, updated 10/23) (updates in 3.05: updated change-of-basis notation in 3.2.4 to be consistent with lectures) |
3.1 ~ Linear Transformations (Definition, Examples, Kernel and Image, Isomorphisms) 3.2 ~ Matrices Associated to Linear Transformations (Definition, Properties, Geometry of Plane Transformations, Change of Basis) |
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| Chapter 4: Inner Products (20pp, v3.00, posted 10/17) | 4.1 ~ Inner Products 4.2 ~ Orthogonality 4.3 ~ Applications of Inner Products |
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| Chapter 5: Eigenvalues and Diagonalization (30pp, v3.00, updated 11/21) (updates in v3.00: added 5.3.2-5.3.4) (updates in v3.05: fixed errors in 5.3.4) |
5.1 ~ Eigenvalues, Eigenvectors, Eigenspaces 5.2 ~ Diagonalization 5.3 ~ Applications of Diagonalization (Markov Chains, Quadratic Forms, Definiteness, Singular Value Decomposition) |
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| Exam Information | |||
|---|---|---|---|
| Exam | Date, Time, Location | Topics | Review Material |
| Midterm 1 Form A, (sols) Form B, (sols) |
Wed, October 6th In Class |
WeBWorKs 1-4 Notes §1.1-1.5 + §2.1-2.6 |
Review Problems, (answers) In-class review on Mon, Oct 4th |
| Midterm 2 Form A, (sols) Form B, (sols) |
Thu, November 4th In Class |
WeBWorKs 5-7 Notes §3.1-3.3 + §4.1-4.2.2 |
Review Problems, (answers) In-class review on Wed, Nov 3rd |
| Midterm 3 Form A, (sols) Form B, (sols) |
Wed, December 1st In Class |
WeBWorKs 8-10 Notes §4.2.3-4.3 + 5.1-5.2 |
Review Problems, (answers) In-class review on Mon, Nov 29th |
| Final | Tue, December 14th 3:30pm-5:30pm 420 Shillman Hall |
WeBWorKs 1-11 Notes §1.1-5.3 The final is COMPREHENSIVE! |
Extra Review Problems, (answers) Review session 1-3pm Fri, Dec 10th (Review slides) |
| Bring your University ID to all exams. Calculators may be used, provided they do not have qwerty keyboards and cannot do symbolic algebra. Cell phones, other electronic devices, books, and notes of any kind will NOT be permitted in exams. | |||
| Old Final Exams |
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| Below are some old final exams from past semesters of Math 2331, which should be fairly representative of the final exam this semester. The time limit for each exam is 2 hours, if you wish to use them for practice. |
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2016 Fall, (solutions) 2017 Spring, (solutions) 2017 Fall, (solutions) 2020 Spring, (solutions) 2020 Fall |
| Tips For Success In This Course | |||
|---|---|---|---|
| Attend Lecture | Missing lecture is a bad idea! If for any reason you cannot make it to a class, you should review notes from someone who did attend. You are responsible for all material covered in lecture. | ||
| Read the Lecture Notes (or Textbook) | The lecture notes and the textbook are comprehensive sources of material for the course. The notes are intended as review material, although many students like to read them as preparation before attending the lecture on the corresponding topics. Please note that the electronic notes are not identical to the material covered in class: this is by design, so as to provide you a slightly different perspective on the material. | ||
| Use WeBWorK Effectively | WeBWorK assignments are intended to help you learn the course material at a basic level. Look over the problems well before the due date, and work on them in concert with the corresponding lectures. You may use technology (calculators, Wolfram Alpha, computer software) and other people to help you (so long as you are submitting your own work), but be mindful: if you do not understand how to do the WeBWorK problems, you will probably struggle on the exams! | ||
| Attend Office Hours | Office hours are specifically reserved for you to receive individual, one-on-one help from the instructor. Office hours will be the most effective when you have already put in effort to learn the material on your own (including trying to solve the homework problems), and when you come in with a list of specific questions or topics you are struggling with. | ||
| Attend Optional Recitation | There is an optional weekly recitation section run by the course's TA, in which the TA will review problems from the course textbook. In addition to seeing additional problems worked out, you may also ask your own questions to the TA. The TA also has weekly office hours, where you may also ask questions. | ||
| Use Tutoring Services | The university offers a wide variety of (free) tutoring services. Please consult the Northeastern Tutoring page for additional information on peer tutoring. The Math Tutoring Center, located in 540B NI, is specifically set up for tutoring in mathematics courses. Tutoring appointments can be made via MyNEU (which will provide lists of available appointments for the tutors for your specific classes); walk-in tutoring is very limited and tends to be unavailable near exam dates. | ||
| Course Schedule | |||
|---|---|---|---|
| The schedule is subject to change! All sections refer to the course lecture notes. | |||
| Week | Schedule | ||
| Week of Sep 6 (class starts 9/8) |
§1.1.1: Systems of Linear Equations §1.1.2: Row-Echelon Form and Reduced Row-Echelon Form §1.1.3: Gaussian Elimination No homework this week. |
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| Week of Sep 13 | §1.2: Matrix Operations §1.3.1: The Inverse of a Matrix WeBWorK 1 due Tuesday 9/14 at 5am. §1.3.2: The Determinant of a Matrix §1.3.3: Cofactor Expansions and the Adjugate §1.3.4: Systems of Linear Equations, Revisited |
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| Week of Sep 20 | §2.1: Vectors in Rn §2.2: The Formal Definition of a Vector Space WeBWorK 2 due Tuesday 9/21 at 5am. §2.3: Subspaces §2.4: Linear Combinations and Span §2.5: Linear Independence and Linear Dependence |
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| Week of Sep 27 |
§2.6.1: Bases of Vector Spaces §2.6.2: Existence of Bases WeBWorK 3 due Tuesday 9/28 at 5am. §2.6.3: Dimension §2.6.4: Finding Bases, Rowspaces, Column Spaces, and Nullspaces §3.1.1: Linear Transformations |
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| Week of Oct 4 |
Review for Midterm 1 WeBWorK 4 due Tuesday 10/5 at 5am. MIDTERM 1 in class Wednesday 10/6 §3.1.2: Kernel and Image |
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| Week of Oct 11 (no class 10/11) |
§3.1.3: Isomorphisms of Vector Spaces §3.2.1: Matrices Associated to Linear Transformations No homework this week. | ||
| Week of Oct 18 |
§3.2.2: Algebraic Properties of Associated Matrices §3.2.3: Geometry of Linear Transformations from R2 to R2 §3.2.4: Change of Basis and Similarity WeBWorK 5 due Tuesday 10/19 at 5am. §4.1.1: Inner Products | ||
| Week of Oct 25 | §4.1.2: The Cauchy-Schwarz Inequality §4.2.1: Orthogonality and Orthonormal Sets §4.2.2: The Gram-Schmidt Procedure, QR Factorization WeBWorK 6 due Tuesday 10/26 at 5am. §4.2.3: Orthogonal Complements | ||
| Week of Nov 1 | §4.2.4: Orthogonal Projection §4.3.1: Least Squares Estimates WeBWorK 7 due Tuesday 11/2 at 5am. Review for Midterm 2. MIDTERM 2 in class Thursday 11/4 |
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| Week of Nov 8 (no class 11/11) |
§4.3.1: Least Squares Estimates §4.3.2: Fourier Series §5.1.1: Eigenvalues and Eigenvectors §5.1.2: Eigenvalues and Eigenvectors of Matrices No homework this week. |
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| Week of Nov 15 | §5.1.3: Eigenspaces §5.2.1: Diagonalizability §5.2.2: Calculating Diagonalizations §5.2.3: The Real Spectral Theorem WeBWorK 8 due Tuesday 11/16 at 5am. | ||
| Week of Nov 22 (no class 11/24-11/26) | §5.3.1: Markov Chains §5.3.2: Bilinear Forms and Quadratic Forms WeBWorK 9 due Tuesday 11/23 at 5am. | ||
| Week of Nov 29 |
Review for Midterm 3. WeBWorK 10 due Tuesday 11/30 at 5am. MIDTERM 3 in class Wednesday 12/1 §5.3.3: Applications of Quadratic Forms, Definiteness | ||
| Week of Dec 6 (class ends 12/8) |
§5.3.4: Singular Values and Singular Value Decomposition Review for Final Exam WeBWorK 11 due Thursday 12/9 at 5am. | ||
| FINAL EXAM 3:30pm-5:30pm, Tue December 14th, 420 Shillman Hall | |||