Math 235 - Introduction to Linear Algebra

Spring 2022

This is the Course Website with specific information for Math 235 Section 8. Information regarding all sections can be found here. We will use Moodle to post some course material and to record grades.

We meet: MWF 9:05 - 9:55 am in LGRT 219

The syllabus is here. It contains the information in this website and a little more.

Most Important Rule:

Ask questions! There are no silly questions!




I endorse Federico Ardila's axioms.

  • Axiom 1. Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

  • Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

  • Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

  • Axiom 4. Every student deserves to be treated with dignity and respect.

Office Hours and Contact Information

  • Instructor: Cristian Rodriguez

  • Email: rodriguez@math.umass.edu

  • Office: LGRT 1341

  • Office Hours:

    • Tuesdays 9:30 - 10:30 am

    • Thursdays 2:00 - 3:00 pm

    • By Appointment. I understand that these days some students prefer to meet remotely. If this is your case, I am happy to schedule a remote meeting using zoom.

Piazza

We will use Piazza as a tool to ask and answer questions electronically. I will add the option to post questions anonymously so that everyone is comfortable asking a question. I strongly suggest to make your questions public because if you have a question it is likely that another student has the same question. To register use the following link with the access code provided in class.


piazza.com/umass/spring2022/math235

Although this tool will be available I believe that the best way for me to answer questions and the best way for you to get a good answer is through office hours or in class.


Required Course Material

  • Textbook: Linear Algebra and Its Applications (5th 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.

Course Outline

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).

Important Dates

  • First day of class .................................... Wednesday, January 26

  • Last day to add/drop ............................. Monday, February 7

  • Holiday - Presidents Day (No Class) .... Monday, February 21

  • Monday schedule ( We meet) ............... Tuesday, February 22

  • Midterm I ................................................ Thursday, March 3

  • Spring Break ........................................... March 13 - March 20

  • Last day to drop with W ......................... Tuesday, March 29

  • Midterm II ............................................... Tuesday, April 12

  • Holiday - Patriots Day (No Class) ......... Monday, April 18

  • Last day of Classes ............................... Wednesday, May 04

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

Grading Policy

  • MyMathLab Homework (20%)

  • Quizzes (15%)

  • Class Participation (5%)

  • Exams (60%): For more information regarding exams you can go here.

    • Midterm I (20%): 7-9pm on Thursday, March 03.

    • Midterm II (20%): 7-9pm on Tuesday, April 12.

    • Final Exam (20%): TBD


For information about Homework and Quizzes go here.

Grading Scale

The course letter-grade scale is:


Accommodation Policy Statement

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.

Academic Honesty

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