Math 235 - Introduction to Linear Algebra

• Instructor: Cristian Rodriguez

• Email: rodriguez@math.umass.edu

• Office: LGRT 1341

• Office Hours:

  • Fridays 9:30 - 10:30 am

  • Wednesdays 1:15 - 2:15 pm

  • By Appointment.

We shifted to Discord!

• Textbook: Linear Algebra and Its Applications (6th edition) by David Lay, Steven Lay, and Judi McDonald.

• Online Homework System: We will use the online homework system MyMathLab. An electronic copy of the textbook is also included in your purchase of MyMathLab. I will provide a handout with details to register in the course in MyMathLab. Use your @umass.edu email when enrolling.

We will roughly cover chapters 1 to 6 of our textbook. You can find the tentative schedule and our class log here.

• Chapter 1 - Linear Equations in Linear Algebra:

Systems of linear equations (1.1), Row reduction and echelon forms (1.2), Vector equations (1.3), The matrix equation Ax = b (1.4), Solutions sets of linear systems (1.5), Linear independence (1.7), Introduction to linear transformations (1.8), The matrix of a linear transformation (1.9).

• Chapter 2 - Matrix Algebra:

Matrix Operations (2.1); The Inverse of a Matrix (2.2); Characterizations of Invertible Matrices (2.3).

• Chapter 3 - Determinants:

Introduction to determinant (3.1); Properties of Determinants (3.2); Cramer’s Rule, Volume and Linear transformations (3.3).

• Chapter 4 - Vector Spaces:

Vector Spaces and Subspaces (4.1); Null Spaces, Column Spaces, and Linear Transformations (4.2); Linearly Independent Sets; Basis (4.3); Coordinate Systems (4.4); The Dimension of a Vector Space (4.4), Rank (4.6); Change of Basis (4.7).

• Chapter 5 - Eigenvalues and Eigenvectors:

Eigenvectors and Eigenvalues (5.1); The Characteristic Equation (5.2); Diagonalization (5.3); Eigen- vectors and Linear Transformations (5.4); Complex Eigenvalues (5.5).

• Chapter 6 - Orthogonality and Least Squares

Inner Product, Length, and Orthogonality (6.1); Orthogonal Sets (6.2); Orthogonal Projections (6.3); The Gram-Schmidt Process (6.4); Least-Squares Problems (6.5 - if time permits).

• First day of class .................................... Tuesday, September 6

• Last day to add/drop ............................. Monday, September 12

• Indigenous People Day (No Class) ..... Monday, October 10

• Midterm I ................................................ Monday, October 17

• Last day to drop with W ......................... Tuesday, November 1

• Midterm II ............................................... Monday, November 21

• Thanksgiving Break ............................... Wednesday, November 23

• Last day of Classes ............................... Monday, December 12

• Final Exam .............................................. TBD

The grade will be computed as follows:

• MyMathLab Homework (15%)

• Quizzes (15%)

• Class Participation (5%)

• Exams (65%): For more information regarding exams you can go here.

  • Midterm I (20%): 7-9pm on Monday October 17.

  • Midterm II (20%): 7-9pm on Monday, October 21.

  • Final Exam (25%): TBD

For information about Homework and Quizzes go here.

The course letter-grade scale is:

UMass Amherst is committed to providing an equal educational oppor- tunity for all students. A student with a documented physical, psychological, or learning disability on file with Disability Services may be eligible for academic accommodations to help them succeed in this course. If you have a documented disability that requires an accommodation, please notify your instructor during the first two weeks of the semester so that we can make appropriate arrangements. Information on services and materials for registering with Disability Services are also available on their website.

We will follow the UMass Code of Conduct. See this link.