## Math 235: Introduction to Linear Algebra

### (Section 4) T,Th 1-2:15 in Goessmann 152

### (Section 3) T,Th 2:30-3:45 in Goessmann 152

**Instructor**: Dr. Liubomir Chiriac, 1115J LGRT (email: chiriac [at] math [dot] umass [dot] edu).

** Office Hours**: Fri 3-4. You can also set up an appointment by sending me an e-mail.

**Textbook and MyMathLab**: * Linear algebra and its applications, 5th Edition* by David Lay, Steven Lay, and Judi McDonald.

An electronic copy of the textbook is included in your purchase of MyMathLab, which is __required__ for this course.

**Homework:** Homeworks will be assigned through MyMathLab.
You should have received a Course ID by now (which is different for every section).

Late assignments can be made up, but with a 50% credit deduction.

**Grading**: Homework and participation - 25%; two Midterms - 25% (each); Final - 25%.

Grades will be assigned to course percentages according to the following scale:

A : 90--100

A- : 87--89

B+ : 84--86

B : 80--83

B- : 77--79

C+ : 74--76

C : 70--73

C- : 67--69

D+ : 64--66

D : 57--63

F : 0--56

**Exam Info**: Past exams are available here.

You are allowed one 8.5" x 11" sheet of notes (both sides).
Calculators and the textbook are not allowed on the exams. You should bring your student ID (UCard) to each exam.

**Make-up Exam Policy**: If you have a documented conflict for one of the exams, in order to take the make-up exam you must give
the course chair Weimin Chen wchen@math.umass.edu (and me) at least one weeks' written notice for a midterm exam and
at least two weeks' written notice for the final exam. Make-up exams will not be given to accommodate travel plans.

**Midterm 1** - Thursday 10/11/18, 7-9PM, location HASA 0020 (Hasbrouck). Covered material: Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8, 1.9, 2.1.

Please work through the practice exam here. The solutions can be found here.

**Midterm 2 **- Tuesday 11/13/18, 7-9PM, location HASA 0020 (Hasbrouck). Covered material: Sections 2.2, 2.3, 3.1, 3.2, 3.3, 4.1, 4.2, 4.3, 4.4, 4.5.

Please work through the practice exam here. The solutions can be found here.

**Final Exam **- Tuesday 12/18/18, 10:30AM-12:30PM, in Boyden Gym. Covered material: Sections 4.5, 4.6, 5.1, 5.2, 5.3, 5.5, 6.1, 6.2, 6.3.

Please work through the practice exam here. The solutions can be found here.

**Syllabus and weekly schedule:** This is an introductory course on linear algebra, covering systems of linear equations, matrices, linear transformations,
determinants, vector spaces, eigenvalues and eigenvectors, and orthogonality.
The schedule below gives the topics from the course text to be covered each week.
(This is only a guideline, and may be modified throughout the term.)

9/4--9/7: 1.1 Systems of linear equations; 1.2 Row reduction and echelon forms; 1.3 Vector equations.

9/10--9/14: 1.3 (continued); 1.4 The matrix equation Ax=b; 1.5 Solution sets of linear systems.

9/17--9/21: 1.7 Linear independence; 1.8 Introduction to linear transformations.

9/24--9/28: 1.9 The matrix of a linear transformation; 2.1 Matrix operations.

10/1--10/5: 2.2 The inverse of a matrix; 2.3 Characterizations of invertible matrices.

10/9--10/12: 3.1 Introduction to determinants; 3.2 Properties of determinants.

10/15--10/19: 3.2 (continued); 3.3 Cramer's rule, volume, and linear transformations; 4.1 Vector spaces and subspaces.

10/22--10/26: 4.2 Null spaces, column spaces, and linear transformations; 4.3 Linearly independent sets and bases.

10/29--11/2: 4.4 Coordinate systems; 4.5 The dimension of a vector space.

11/5--11/9: 4.6 Rank; 5.1 Eigenvectors and eigenvalues.

11/13--11/16: 5.1 (continued); 5.2 The characteristic equation.

11/19--11/23: Thanksgiving break.

11/26--11/30: 5.3 Diagonalization; 5.5 Complex eigenvalues.

12/3--12/7: 6.1 Inner product, Length, and Orthogonality; 6.2 Orthogonal sets, 6.3 Orthogonal projections.

12/10--12/12: Review.