Math 235 : Introduction to Linear Algebra

Spring 2020

This is the course-wide webpage. Please consult your section webpage for additional information.


Overrides

Students needing an override in order to enroll in the course should contact the course chair Weimin Chen wchen@math.umass.edu with the following information: (1) sections of the course which conflict with other courses from your academic schedule, and (2) preferred section of the course. (Unfortunately, in order to keep the sections balanced we cannot guarantee that you will be assigned to your preferred section.)


Sections

235.1. Rafael Montezuma, MWF 1:25PM-2:15PM.
235.2. Rafael Montezuma, MWF 11:15AM--12:05PM.
235.3. Laura Colmenarejo, TuTh 11:30AM--12:45PM.
235.4. Alexei Oblomkov, TuTh 10:00AM--11:15AM.
235.5. Jonathan Simone, MWF 10:10AM--11:00AM.
235.6. Weimin Chen, TuTh 2:30PM--3:45PM.
235.7. Ivan Mirkovic, TuTh 1:00PM--2:15PM.
235.8. Jennifer Li, TuTh 8:30AM--9:45PM.
235.9. Angelica Simonetti, MWF 1:25PM--2:15PM.


Textbook and Online homework

The course text is Linear algebra and its applications (5th edition) by David Lay, Steven Lay, and Judi McDonald.

MyMathLab is required for this course. An electronic copy of the textbook is included in your purchase of MyMathLab. Go to www.mymathlab.com (link) and use the Course ID for your own section (provided by your section's instructor).

Online homework and quizzes will be assigned through MyMathLab by your instructor.


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 by your instructor as necessary.)


1/20--1/24: 1.1 Systems of linear equations; 1.2 Row reduction and echelon forms; 1.3 Vector equations.

1/27--1/31: 1.3 (continued); 1.4 The matrix equation Ax=b; 1.5 Solution sets of linear systems.

2/3--2/7: 1.7 Linear independence; 1.8 Introduction to linear transformations.

2/10--2/14: 1.9 The matrix of a linear transformation; 2.1 Matrix operations.

2/17--2/21: 2.2 The inverse of a matrix; 2.3 Characterizations of invertible matrices.

2/24--2/28: 3.1 Introduction to determinants; 3.2 Properties of determinants.

3/2--3/6: 3.2 (continued); 3.3 Cramer's rule, volume, and linear transformations; 4.1 Vector spaces and subspaces.

3/9--3/13: 4.2 Null spaces, column spaces, and linear transformations; 4.3 Linearly independent sets and bases.

3/16-3/20: Spring break.

3/23--3/27: 4.4 Coordinate systems; 4.5 The dimension of a vector space.

3/30--4/3: 4.6 Rank; 5.1 Eigenvectors and eigenvalues.

4/6--4/10: 5.1 (continued); 5.2 The characteristic equation.

4/13--4/17: 5.3 Diagonalization; 5.5 Complex eigenvalues.

4/20--4/24: 6.1 Inner product, Length, and Orthogonality; 6.2 Orthogonal sets, 6.3 Orthogonal projections.

4/27--4/29: 6.3 (continued), 6.4 The Gram--Schmidt process.


Exams

There will be two midterm exams and a final exam. 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.

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 at least one weeks' written notice for a midterm exam and at least two weeks' written notice for the final exam. Other make-up exams (for example due to medical emergencies) will be handled by your section instructor. Make-up exams will not be given to accommodate travel plans.

First midterm exam

The first midterm will be held on Thursday 2/27/20, 7:00PM--9:00PM, at the following locations:

Sections 1,3,9 (Montezuma, Colmenarejo, Simonetti). HASA0020
Sections 2,4,5 (Montezuma, Oblomkov, Simone). MAH0108
Sections 6,7,8 (Chen, Mirkovic, Li) ISB0135

The syllabus for the first midterm is the following sections of the textbook: 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 of the practice exam are here.

Second midterm exam

The second midterm will be held on Thursday 4/9/20, 7:00PM--9:00PM, at locations TBA

The syllabus for the second midterm is the following sections of the textbook: 2.2, 2.3, 3.1, 3.2, 3.3, 4.1, 4.2, 4.3, 4.4, 4.5.

Final Exam

The date, time and location of the final exam are TBA by the university.



Grading

Your course grade will be computed as follows: First midterm exam 25%; Second midterm exam 25%; Final exam 25%; Homework, quizzes, and class participation 25% (determined by your section instructor).

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


Accommodation Policy Statement

UMass Amherst is committed to providing an equal educational opportunity 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.


Academic Honesty Statement

Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst. Academic dishonesty is prohibited in all programs of the University. Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty. Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty. Instructors should take reasonable steps to address academic misconduct. Any person who has reason to believe that a student has committed academic dishonesty should bring such information to the attention of the appropriate course instructor as soon as possible. Instances of academic dishonesty not related to a specific course should be brought to the attention of the appropriate department Head or Chair. Since students are expected to be familiar with this policy and the commonly accepted standards of academic integrity, ignorance of such standards is not normally sufficient evidence of lack of intent (http://www.umass.edu/dean_students/codeofconduct/acadhonesty/).


Gen. Ed. statement for Math 235

MATH 235 is a three-credit General Education course that satisfies the R1 (Basic Math Skills) and R2 (Analytic Reasoning) general education requirements for graduation.

The General Education Program at the University of Massachusetts Amherst offers students a unique opportunity to develop critical thinking, communication, and learning skills that will benefit them for a lifetime. For more information about the General Education Program, please visit the GenEd web page.

Learning Outcomes for all General Education courses:

Math 235 satisfies the following General Education objectives:

Content:  Know fundamental questions, ideas, and methods of inquiry/analysis used in mathematics: Students will learn to analyze linear systems, transformations, and spaces using matrices. In learning Linear Algebra, students will develop abstract reasoning skills to understand higher dimensional systems and spaces that we cannot directly visualize.

Critical Thinking: Students demonstrate creative, analytical, quantitative, & critical thinking through inquiry, problem solving, & synthesis: Students will use critically thinking skills to develop and understand the theory of matrices and the linear systems, transformations, and spaces that they represent, as well as computational skills to analyze these matrices efficiently.

Communication: Develop informational and technological literacy: Students will develop their writing skills by articulating their reasoning of computations made and writing formal proofs during the course.

Demonstrate capacity to apply disciplinary perspectives and methods of analysis to real world problems (the larger society) or other contexts: Real-world and theoretical applications across all fields can be represented, or estimated, in Linear Algebra by matrices. Students will learn logical and computational methods to analyze these matrices.

Learning Outcomes for the R1 and R2 Designations:

Because Math 235 presupposes basic math skills, it carries the designation for the Basic Math Skills requirement (R1). In addition, the course satisfies the following objectives of the Analytic Reasoning requirement (R2):

Advance a student's formal or mathematical reasoning skills beyond the level of basic competence:  In learning Linear Algebra in Math 235, students will think critically and advance their mathematical reasoning skills by analyzing matrices and the linear systems, transformations, and spaces that they represent.

Increase the student's sophistication as a consumer of numerical information:  Linear Algebra provides an efficient, yet abstract, way to analyze numerical information from concepts across mathematics. Applications across all fields can be represented, or estimated, by matrices. Students will form these connections between mathematical theories and linear algebra, as well as learn methods within linear algebra to make related formal computations.




This page is maintained by Weimin Chen wchen@math.umass.edu