Math 110.201 Linear Algebra

Fall 2013 Course Syllabus

http://www.mathematics.jhu.edu/brown/courses/f13/201.htm

 

Dr. Richard Brown

MWF 10:00pm - 10:50pm: Bloomberg 272

brown@math.jhu.edu

 

403 Krieger Hall

 

410-516-8179

 

Office Hours:

 

M

1:00-2:00 pm

by appt. other times

W

1:00-2:00 pm

 

Text Linear Algebra with Applications, 5th Edition, Otto Bretscher, New Jersey: Pearson, December, 2012 0321796977 978-0321796974

 

Current Recitation Sections:

Section

Time

Place

Instructor

1

Tuesday 1:30pm

Hodson 211

Mogni

2

Tuesday 3:00pm

Krieger 300

Grounds

3

Tuesday 4:30pm

Krieger 302

Grounds

4

Thursday 1:30pm

Krieger 304

Mincheva

5

Thursday 3:00pm

Bloomberg 274 Mincheva

Course Material: The core of the course will center on the text material, and will basically cover the material detailed in the syllabus link below.  I may add and/or slightly alter this material depending on how the semester plays out.  But the core set of material that I will cover will be what is on the syllabus:

Official Syllabus for 110.201 Linear Algebra

In addition to this, you should be aware that the prerequisite for this is a full year of single variable calculus.  With an Advanced Placement BC exam score of 5, or the equivalent credits of the course 110.109 Calculus II (Phys Sci & Eng), you are considered prepared for this course.  If there is a question, please come see me.  For now, what we consider prerequisite content is everything on the syllabus for 110.109.  The link is here:

Official Syllabus for 110.109 Calculus II (Phys Sci & Eng)

Grade Policy:  There will be weekly homework sets and possibly some projects (20%), 2 in-lecture exams (40%) and a final (40%).  The schedule of these exams is given with the homework problems below. There will be no make-ups on homework or exams.  If you will not be present when homework is submitted, please submit the assignment early.  If you miss a homework or project deadline, you can talk to the TA for late acceptance, but I have instructed them to not accept late submissions.  If you miss an exam, you will have to be cleared by me to be excused from the exam, a process that will include documentation and a valid excuse.  In this case the ultimate grade for that exam will be calculated based on your performance on future exams and the final. 

Homework: Homework based on the week’s lectures will be posted as official on the course web site sometime on Friday (Homework may be posted earlier, but may change as the lectures evolve for the week). That assignment will be due in lecture at the end of the following week.  See below for the due dates.  Homework is an absolutely essential educational part of the course. You will be graded mostly on your ability to work problems on exams. You cannot work problems on exams if you have not practiced the techniques and become comfortable applying the concepts within the homework problems. If you misuse homework by not doing it yourself, or not checking that you can solve a problem on your own after having been shown how to do it, then your exam scores and corresponding grade will reflect this. Trust me on this last point.  Talk to your section Teaching Assistant about how to turn in a homework if you cannot go to class. Some additional points:

  • You are strongly encouraged to collaborate in the analysis and study stage of homework preparation.  However, you are required to submit completely original work, however, and must write up your homework for final submission alone.

  • You will be graded on your PROCESS in homework construction rather than simply your ability to calculate.  You must present your homework solutions as if they are complete educational tools for study.  In essence, you must PRESENT your solution and not simply answer questions. 

  • Here is a brief idea of how one should construct homework problems for submission:

How to construct homework problem solutions

Course Policy: You are responsible for lecture notes, any course material handed out, and attendance in class.  While I will not formally record your attendance, I will get to know you and your rate of presence over time.  The lectures will be conducted as if you have already read the material and attempted some homework problems.  In this manner, you can focus mainly on those parts of the lectures that cover the areas of your reading you found difficult to understand. My teaching style is that of interactive discussion and I will rely on your input in developing the material.  Active participation in the classroom is a great way to generate the discussion necessary to fully grasp the material.

 

Help Room:  213 Kreiger Hall.  The hours are 9am  9pm on Monday through Thursday, and 9am  5pm on Friday.  This free service is a very valuable way to get one-on-one help on the current material of a class from other students outside the course.  It is staffed by graduate students and advanced undergraduates.

Ethics Statement:  The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful.  Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies.

Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the Internet and electronic devices unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse.

In this course, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged.  Your ability to talk mathematics is of particular importance to your general understanding of mathematics.

You should collaborate with other students in this course on the general construction of homework assignment problems.  However, you must write up the solutions to these homework problems individually and separately.  If there is any question as to what this statement means, please see the professor or the grader.

For more information, see the guide on "Academic Ethics for Undergraduates" and the Ethics Board web site (http://ethics.jhu.edu).

Students with Disabilities:  Students with documented disabilities or other special needs that require accommodation must register with the Office of Academic Advising. After that, remind me of your needs at least 5 days prior to each exam; we will need to have received confirmation from Academic Advising.

Fall 2013 Tentative Schedule

The details of this material will be updated and reformed as the semester progresses. 

 

Week

Sections

Homework

Due in Lecture

September 4 -- 6

 

 

Course Orientation

 

September 13

How to present....

1.1 Introduction to Linear Systems

1.2 Matrices, Vectors, and Gauss-Jordan

1.3 Linear Systems Solutions

18,21,27,31

2,11,18,20,29,48,49,EP1,EP2

1,5 (Note:  EP problems are below chart)

September 9 -- 13

Sep09, Sep11, Sep13

1.3 Linear Systems Solutions

2.1 Linear Transformations

2.2 Geometric View

24,26,36,37,55

6,8,13,19-22,63

1,4,8,10,18,20,26,30,42,45

September 20

2.1.13a

September 16 -- 20

Sep16, Sep18, Sep20

 

2.3 Matrix Products

2.4 The Inverse of a Linear Transf.

3.1 Image and Kernel

14,17,20,23,29,30,46,56,62,EP3

2,4,7,8,16,17,22,24,26,30,32,52,56,58,60,76

September 27

Some Solutions

September 23 -- 27

Sep23, Sep25, Sep27

3.1 Image and Kernel

3.2 Subspaces of $\mathbb R^n$

3.3 The Dimension of a subspace

1,4,6,9,18,20,24,26,27,30,34,44

1-3,6,8,16,24,32,34,46,47,49

October 4

Some Solutions

September 30 -- October 4

Sep30, Oct02, Oct04

3.3 The Dimension of a subspace

3.4 Coordinates

6,10,22,28,30,32,33,35

6,10,15,20,26,37,44,46,48,53,56,69

October 11

Some Solutions

October 7 -- 9

Oct07, Oct09

4.1 Introduction to Linear Spaces

1-5,10,11,18,19,20,24,27,32,49

October 18

Some Solutions

October 11

Exam 1 (Sections covered thru 3.4)

Exam Solutions
October 14 Fall Break:  No Class
October 15, 16 -- 18

Oct15, Oct16, Oct18

4.2 Linear Transf. & Isomorphisms

4.3 The Matrix of a Linear Transf.

1,3,6,17,19,22,25,30,32,38,52,54

1-3,16,22,29,32,48,49,52

October 25

October 21 -- 25

Oct21, Oct23, Oct25

5.1 Orth. Projections/ Orthon. Bases

5.2 Gram-Schmidt and QR Factor.

2,6,8,10,16,17,26,28

4,8,16,18,26,28,32,34,38

November 1

October 28 -- November 1

Oct28, Oct30, Nov01

5.3 Orthogonal Transf. & Matrices

5.5 Inner Product Spaces

1-4,34,36,40,44,52,53,60

1,4,8,9,10,14,20,24

November 8

November 4 -- 8

Nov04, Nov06, Nov08

6.1 Introduction to Determinants

6.2 Properties of Determinant

6.3 Geometric Interp. of Determinant

8,16,17,26,30,34,38,43,49,52,59

8,10,12,16,17,18,24,27,28,45,47

November 15

November 11 -- 15

Nov11, Nov13, Nov15

6.3 Geometric Interp. of Determinant

7.1 Diagonalization

7.2 Finding the Eigenvalues

1,2,4,9,11,13,14

1-4,10,12,15,19,40,41,50,56

2,8,10,15

November 22

November 18 -- 22

Nov18, Nov20, Nov22

7.3 Finding the Eigenvectors

7.5 Complex Eigenvalues

4,6,16,20,21,22,24,27,34,36,42,50,51,52

15,19,20,24,25,28,30

December 2

Some Solutions

November 25  Nov25

8.1 Symmetric Matrices

 

Not to be handed in

November 27 -- December 1

Thanksgiving Break:  No classes

December 2    Dec02

8.2 Quadratic Forms

 

Not to be handed in

December 4

Exam 2 Sections covered (Solutions)

December 6

Course Review

 

 

 

December 11

Final Exam

9:00am - 12:00pm: Bloomberg 272

 

Extra Problems: 

  1. In class was a definition of the graph of a linear equation in three variables as an object living in three-space.  For a similar definition for the graph of a linear equation in $n$-variables living in $n$-space.  Be careful to specify any constraints on the coefficients.
  2. In the system given in class, the graphs of the first two equations $3x+5y+3z = 25$ and $7x+9y+19z = 65$ intersect in a line.  Find a parameterization for this line as it sits in $\mathbb R^3$, by setting $z$ to be the variable $t$ (so that $z(t) = t$), and calculating $x(t)$ and $y(t)$.  Show that the solution to the system $(x,y,z)= (4,2,1)$ is on this line, and calculate the value of $t$ that corresponds to it.
  3. As best as you can, answer the question posed in class:  Can a non-square matrix $\mathbf A_{n\times m}$, where $n\not= m$, have an inverse? As hints, we also ask:  (1) If $m>n$, can the linear transformation $T(\mathbf x) = \mathbf A\mathbf x$ be one-to-one? And (2) for $n>m$, can the linear transformation $T(\mathbf x) = \mathbf A\mathbf x$ possibly be onto?