MATH 233: Linear Algebra I

There is no required text for this course. However, if you need or want a supplemental resource to study from, here are a few suggestions:

A First Course in Linear Algebra, by Lyryx Learning based on the original text by K. Kuttler. (free online textbook)

Linear Algebra with Applications, by W. Keith Nicholson. (free online textbook)

Linear Algebra, by Jim Hefferon. (free online textbook)

Linear Algebra and its Applications, by David Lay. (This is an exceptional textbook on linear algebra.)

Please note that it is a good idea to work on developing your independent reading skills. It would be a good idea to read the textbook as a supplement to our in-class work. You should read the sections of the textbook which correspond to the material covered during the lectures. The reading will enable you to answer my questions and ask your own focused questions during lectures and help you to better understand the material. There may be slight differences in terminology and definitions between the textbooks and what we learn in class. When this occurs, use the in-class terminology and definitions.

A calculator is NOT required for this course, and you will not be able to use one during exams. It may be helpful to make use of a calculator (or mathematical programs such as MATLAB, Maple, or Mathematica) on homework. However, our primary use of technology will be java applets and visualization tools freely available on the internet.

Topics covered: Topics include linear equations, matrices, linear transformations, determinants, eigenvalues, eigenvectors, and various applications.

For many of you, the material covered in this course will be new. Definitions are extremely important in this course. Be prepared to memorize a lot of them. Besides demonstrating competence in learning definitions, theorems, and problem-solving techniques of elementary linear algebra, you will also be required to demonstrate the ability to do simple proofs on homework and exams.

The notions of linear algebra are fundamental in almost all higher mathematics. In calculus courses the concept of a function is what one arrives at after studying graphs or simple mechanical motion in physics and stripping away the information which is not essential to doing calculations. Similarly, the ideas studied in linear algebra are what comes from stripping away the unnecessary information involved in solving simultaneous equations, studying systems of differential equations, higher order differential equations, multivariable calculus, as well as the physics of three (or four or higher) dimensional space and advanced econometrics models. Just as a function is a higher level of abstraction than the quantity the function represents, matrices, linear transformations, and vector spaces are more abstract than the functions, equations, or physical or economic situations which they represent.

Upon successful completion of this course, a student will be able to:

• Solve systems of linear equations,
• Analyze vectors in Rⁿ geometrically and algebraically,
• Recognize the concepts of the terms span, linear independence, basis, and dimension, and apply these concepts to various vector spaces and subspaces,
• Use matrix algebra and the relate matrices to linear transformations,
• Compute and use determinants,
• Compute and use eigenvectors and eigenvalues,
• Determine and use orthogonality, and
• Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of linear algebra concepts.

Your overall grade will be determined as follows:

• 19% - WeBWorK, Quizzes, and Class Participation
• 27% - Exam 1
• 27% - Exam 2
• 27% - Final Exam

Your overall grade for the course will reflect how well the class is doing, and will be high if everyone is working hard on the homework and doing well on the exams. Almost all the questions on the exams will be in the same spirit with the homework questions. Therefore understanding how to do all the homework questions will enable you to do well on the exams.

Homework: Most homework will be done through the internet-based homework system called WeBWorK. However, there may occasionally be problems you must write out and hand in to me. All assignments must be completed by the given due date. Moreover, while it is not required that you complete a handwritten version of WeBWorK assignments, it is strongly encouraged. Writing a problem out by hand, showing all calculation steps, and keeping them collected in a notebook will greatly assist you as you prepare for exams.

Exams: There will be two Midterm Exams and one Final Exam. Exams are closed book, closed notes, closed friends, and open brain. Cell phones and other electronic devices will NOT be permitted in exams. Whether or not calculators are allowed on an exam will be determined at a later time.

Quizzes and Class Participation: There will be occasional, unannounced quizzes in class to make sure students are understanding and keeping up with the course material. Quizzes will be based on material from homework and previous lectures. It is also imperative that you keep up with reading the textbook. NO MAKE-UP QUIZZES WILL BE GIVEN. Class participation will be based on your willingness to ASK and ANSWER questions in class.

It is essential not to fall behind because each lecture is based on previous work. If you have trouble with some material, SEEK HELP IMMEDIATELY in the following ways:

Accommodations: SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional, or cognitive disabilities. Accommodations will be made for medical conditions related to pregnancy or parenting. Requests for accommodations including letters or review of existing accommodations should be directed to Ms. Heather Packer in the Office of Disability Services in Erwin Hall 22 or disabilityservices@geneseo.edu or 585-245-5112. Students with letters of accommodations should submit a letter to each faculty member at the beginning of the semester and discuss specific arrangements. Additional information is available at the Office of Disability Services.