Math 212
Linear Algebra

Extended Summer Session 2003

Instructor: Dr. John G. Del Greco
The map L(s,t) = (s-t, s+t-1/2) as plotted by Maple  


Course Information

John G. Del Greco, Ph.D.
Damen Hall, Room 330F
Office Hours:
Tuesdays and Thursdays, 4:00p.m.-5:00p.m., Damen Hall, Room 330F
Telephone Numbers:
E-mail Address:
Math 212 World Wide Web Site:
Class Hours and Location:
Tuesday and Thursday evenings, 6:00p.m.-7:45p.m., Damen Hall, Room 429
Math 132 or Math 162.
Linear Algebra and Its Applications (3rd edition) by David C. Lay. The text is available at Beck's Bookstore on Sheridan Road.
Other Recommended Texts:
There are a number of recommended linear algebra texts:
Calculators will be allowed on the tests and final examination.
Attendance is not required. Students are responsible for all material discussed in class whether choosing to attend class or not. In addition, handouts will be distributed only once. Students not attending class may have to obtain copies of any handouts from fellow classmates. The instructor generally recycles any extra handouts immediately after the class in which they were distributed. Students may obtain copies of the handouts online. Some of the handouts are in .pdf format. A reader for .pdf files (called Acrobat files) can be obtained from the Adobe web site.
Classroom Etiquette:
To maintain a proper atmosphere for learning, the following standards of classroom behavior will be observed.
Final grades will be computed according to the following recipe.

(1.) There will be a final examination worth 30%. The final examination will cover all the topics in the course.

(2.) There will be three tests each worth 20%. Therefore, the tests will be worth 60% of the total grade. Each test will be extend over the entire class period.

(3.) Homework problems will be assigned from the textbook and must be completed before the conclusion of the next class. Problems from the text will be announced in class and will also be posted on the web. Homework will be collected and graded. Late homeworks will not be accepted under any circumstances. Homework solutions will be distributed in class. The homework assignments will account for the remaining 10% of the final grade.

Tests and Homeworks
Weight in Final Grade
Test #1 20% June 5, 2003
Test #2 20% June 26, 2003
Test #3 20% July 17, 2003
Homework 10% N/A
Final Exam 30% August 7, 2003

Final course grades will be assigned according to the scale below.

Average Grade
90%-100% A
87%-89% B+
80%-86% B
77%-79% C+
70%-76% C
67%-69% D+
57%-66% D
0%-56% F

No exceptions to the grade scale will be made for students expecting to graduate. In addition, a student's financial arrangements with Loyola University or other funding agencies is his or her own business. No consideration will be given to these matters by the instructor when assigning final grades.

Students can access their grades online.
Extra Credit and Grade Curve:
There will be no extra credit (per student) given in the course. There may be a curve of final grades depending on the overall performance of the class. Students should not expect that a grade curve will automatically applied to final grades. A curve, if given, would only have a positive impact on a student's raw (uncurved) course average.
Missed Test Policy:
Students may miss tests and examinations without penalty only if they are unable to attend class because of illness. The illness must be serious enough to require a visit to a physician. A note from the student's physician is necessary to be eligible to take a make-up test or examination.
Course Goal:
The goal of the course is to acquaint the student with some of the results and techniques of linear algebra. In particular, the course will serve as a bridge to more advanced courses in mathematics and computer science.
Important Dates:
Monday, July 7 (5:00p.m.) is the last day a student may withdraw from a course with a non-penalty grade of W. Thursday, August 7 is the last day of class in Math 212. All Loyola University schedules and calanders are available online.
Academic Dishonesty:
Prohibited activity includes cheating on a test or examination, using forbidden materials on a test or examination and helping others on a test or examination. A student who violates these rules for the first time will receive a failing grade on the test or examination on which the cheating occurred. A second violation will result in an F for the entire course.

Course Schedule

The following schedule is tentative. The instructor reserves the right to alter the schedule to accommodate the needs of the class.
  1. Systems of Linear Equations
    1. Systems of linear equations and echelon forms (Sections 1.1 and 1.2)
    2. Vector and matrix equations (Sections 1.3 and 1.4)
    3. Solutions of linear systems (Section 1.5)
    4. Linear independence (Section 1.7)
    5. Linear transformations and matrices (Sections 1.8 and 1.9)
  2. Matrix Algebra
    1. Matrix operations (Sections 2.1)
    2. Matrix inverses (Section 2.2 and 2.3)
  3. Determinants
    1. Determinants (Section 3.1)
    2. Properties of determinants (Section 3.2)
    3. Cramer's rule (Section 3.3)
  4. Vector Spaces
    1. Vector spaces and subspaces (Section 4.1)
    2. Null spaces, column spaces and linear transformations (Section 4.2)
    3. Linear independence and bases (Section 4.3)
    4. Coordinate systems (Section 4.4)
    5. Dimension and rank (Sections 4.5 and 4.6)
    6. Change of basis (Section 4.7)
  5. Eigenvalues and Eigenvectors
    1. Eigenvectors and eigenvalues (Section 5.1)
    2. Characteristic equation (Section 5.2)
    3. Diagonalization (Section 5.3)
    4. Eigenvalues and linear transformations (Section 5.4)