This is the webpage for MATH 2940-002 ONLY. Sections 001 and 002 are entirely independent: different instructors, syllabi, assignments, and exams. This summer, MATH 2940-001 is using Blackboard.
Meeting time: MTWThF 10-11:15 am
Location: Malott Hall 207
Instructor: Daniel Jerison
Office: Malott Hall 581
Office hours: MW 11:15 am - 12:15 pm or by appointment Office hours Wednesday, August 10, 10 am - 12 pm
Email: jerison at math.cornell.edu
TA: Sergio Da Silva
Office hours: Th 7:45-9:45 am, Malott Hall 218, or by appointment
Email: smd322 at cornell.edu
This is a very fast-paced class. We will cover all the material of a full-semester linear algebra course in only six weeks. For this reason, keeping up with the course material is of paramount importance. Attendance will not be taken, but I strongly encourage you to come to class every day.
The best way to learn is by solving problems. Classes will include lectures and periods of time for you to work on exercises with your classmates. Outside of class, I may assign parts of the textbook for you to read before the following day's meeting. These readings will be in addition to the assigned homework problems. Overall, you should expect to spend 2 to 3 times as many hours on this class as you would on a similar course during the academic year.
In case you are having trouble understanding a topic, do not wait! Come to office hours and ask questions during class or via email. Office hours are an excellent opportunity to go into greater depth on whichever concepts you need help understanding. The course material builds on itself, so a solid grasp of the earlier material is essential for you to learn and appreciate the later topics.
Linear algebra and its applications. Topics include matrices, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and inner product spaces. Applications include brief introductions to difference equations, Markov chains, and systems of linear ordinary differential equations.
Due to an overlap in content, students will receive credit for only one course in the following group: MATH 2210, MATH 2230, MATH 2310, MATH 2940. Taking MATH 2930 and 2940 simultaneously is not recommended.
Note: The official course description says: "May include computer use in solving problems." That will not be a part of the course this summer. In addition, MATH 1920 (multivariable calculus) is listed as a prerequisite. In fact there is very little overlap between the two courses, so you can take MATH 2940 without having previously taken MATH 1920.
Linear Algebra and its Applications by Lay, Lay, and McDonald, 5th edition. Can be purchased online for around $30-50; see these links.
15%: Homework
22.5%: Prelim 1
22.5%: Prelim 2
40%: Final exam
All exams are closed-book and closed-notes; no calculators or similar aids are allowed. You must take the exams at the scheduled times.
Prelim 1: Tuesday, July 12, in class.
Prelim 2: Tuesday, July 26, in class.
Final exam: Tuesday, August 9, 8:30-11 am in Malott Hall 207.
Prelim 1 covers all course material through Friday, July 8. This includes sections 1.1-1.5, 1.7-1.9, 2.1-2.3, 2.5 (up to the end of p.127), 3.1-3.2, and 3.3 (from Theorem 9 to the end, not including Cramer's Rule). Practice problems and solutions. Actual exam and solutions.
Prelim 2 covers the course material from after Prelim 1 through Friday, July 22. This includes sections 4.1-4.6, 4.8-4.9, 5.1-5.4, and 5.6-5.7. Not included: the end of section 4.8 (starting from "Nonhomogeneous Equations"), the start of section 5.4 ("The Matrix of a Linear Transformation" section). Practice problems and solutions. Actual exam and solutions.
The final exam covers all the course material, with a greater emphasis on Chapters 6 and 7. This includes everything from the two prelims along with sections 6.1-6.5, the "Least-Squares Lines" part of section 6.6, 6.7, 7.1-7.2, and 7.4. Practice problems and solutions.
You are encouraged to work with each other on the homework. Everything you write should be in your own individual words; direct copying is forbidden! You are not allowed to get help from any other person or source on an exam, including the textbook, unless that exam's instructions specifically permit it.
It is Cornell policy to provide reasonable accommodations to students who have a documented disability (e.g., physical, learning, psychiatric, vision, hearing, or systemic) that may affect their ability to participate in course activities or to meet course requirements. Students with disabilities are encouraged to contact Student Disability Services and their instructors for a confidential discussion of their individual need for academic accommodations. Student Disability Services is located in 420 CCC. Staff can be reached by calling 607-254-4545.
Subject to change.
June 27, 28, 29: Sections 1.1-1.5. HW 1 due Friday, July 1.
June 30, July 1, 5: Sections 1.7-1.9, 2.1, start of 2.2. HW 2 due Thursday, July 7.
July 6, 7, 8: Finish section 2.2, sections 2.3, 2.5, 3.1-3.3. Handout: Invertible matrices. Handout: Determinants and row operations. HW 3 due Monday, July 11.
July 11: Prelim 1 review.
July 12: Prelim 1.
July 13, 14, 15: Sections 4.1-4.5. HW 4 due Monday, July 18.
July 18, 19: Sections 4.6, 4.8-4.9. HW 5 due Thursday, July 21.
July 20, 21, 22: Sections 5.1-5.4, 5.6-5.7. HW 6 due Monday, July 25.
July 25: Prelim 2 review.
July 26: Prelim 2.
July 27, 28, 29: Sections 6.1-6.4. HW 7 due Monday, August 1.
August 1, 2, 3: Sections 6.5, start of 6.6, 6.7, 7.1-7.2. HW 8 due Friday, August 5. Handout: Symmetric matrices have real eigenvalues.
August 4: Section 7.4. No required HW from this section, but see optional exercises below. The Wikipedia page for singular value decomposition has a useful animation that goes through the steps of a SVD for a 2 × 2 matrix.
August 5: Final exam review.
August 9: Final exam.
Homework is due at the beginning of class on the due date. Solutions will be posted later the same day. Late homework will not be accepted. However, your lowest homework score will be dropped.
HW 1: Due Friday, July 1. Exercises 1.1.25 (hint: start doing row operations and see whether things are zero or not), 1.2.12, 1.2.19, 1.2.28, 1.3.8, 1.3.25, 1.4.1, 1.4.16, 1.5.7, 1.5.31. Solutions.
HW 2: Due Thursday, July 7. Exercises 1.7.30, 1.7.36, 1.8.15, 1.8.17, 1.9.9 (hint: follow what happens to the standard basis vectors e1, e2), 1.9.35, Required additional problems, 2.1.1, 2.2.7, 2.2.24, 2.2.35. Solutions to textbook exercises and additional problems.
HW 3: Due Monday, July 11. Exercises 2.3.15, 2.3.22, 2.3.27, 2.5.4, 3.1.10, 3.2.7, 3.2.24 (hint: see the solution to Practice Problem 2), 3.2.31, 3.3.20, 3.3.27. Solutions.
HW 4: Due Monday, July 18. Exercises 4.1.13, 4.1.19, 4.2.8, 4.2.16, 4.3.11, 4.3.14, Required additional problems, 4.4.3, 4.4.11, 4.4.13 (hint: see the solution to Practice Problem 2), 4.5.13. Solutions to textbook exercises and additional problems.
HW 5: Due Thursday, July 21. Exercises 4.6.2, 4.6.21, 4.8.6, 4.8.21, 4.9.3, 4.9.13. Solutions.
HW 6: Due Monday, July 25. Exercises 5.1.12, 5.1.25, 5.1.35, 5.2.12, 5.3.6, 5.3.13, 5.4.8, 5.4.17, 5.4.23, 5.6.5, 5.6.9, 5.7.5, Required additional problem. For exercise 5.7.5, draw typical trajectories even if the origin is not a saddle point. Solutions to textbook exercises and additional problem.
HW 7: Due Monday, August 1. Exercises 6.1.14, 6.1.28, 6.1.30, 6.2.10, 6.2.28, 6.3.10, 6.3.16, 6.3.17, 6.4.2, Required additional problems. For 6.2.28, an orthogonal matrix is a square matrix whose columns are orthonormal. This is standard terminology, unfortunately. Solutions to textbook exercises and additional problems.
HW 8: Due Friday, August 5. Exercises 6.5.4, 6.5.8, 6.5.10, 6.6.2, 6.7.23, 6.7.25, 7.1.19, 7.1.23, 7.2.6, 7.2.13. Solutions.
Exercises from section 7.4 (not to turn in): 7.4.6, 7.4.13 (hint: see the solution to Practice Problem 1), 7.4.18. Solutions.