MATH332 Linear Algebra

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=Course Information=
 
=Course Information=
  
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Systems of linear equations, matrices, determinants and eigenvalues. Linear operators. Abstract vector spaces. Applications selected from linear programming, physics, graph theory, and other fields.
+
MATH332: Linear Algebra - Systems of linear equations, matrices, determinants and eigenvalues. Linear operators. Abstract vector spaces. Applications selected from linear programming, physics, graph theory, and other fields.
 
Prerequisite: MATH 213, 223 or 224.
 
Prerequisite: MATH 213, 223 or 224.
−
3 hours lecture; 3 semester hours. .
 
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−
==Course Calendar==
 
−
 
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[http://www.google.com/calendar/embed?src=retasd1tmvosjsek0o0avfd6ds%40group.calendar.google.com&ctz=America/Denver  Advanced Engineering Mathematics Calendar]
 
  
 
==Instructor Information ==
 
==Instructor Information ==
Line 22: Line 14:
 
Office Phone : 303.384.2446
 
Office Phone : 303.384.2446
  
−
email : math348@gmail.com
+
email : math332.summer2010@gmail.com
  
−
Office Hours :
+
==Course Calendar ==
 +
Classes Begin : June 28th, 2010
 +
 
 +
Meeting Days : Monday, Tuesday, Wednesday, Thursday
 +
 
 +
Course Sections :
 +
    Section A,  3:00pm-4:20pm, Green Center 249
 +
 
 +
 
 +
Classes End : August 19th, 2009
 +
 
 +
Important Dates :
 +
    July 5th - No Class
 +
    July  6th - Last Day to Withdrawal  (Without a W)
 +
    August 6th - Last Day to Withdrawal
 +
 
 +
==Office Hours ==
 +
 
 +
Fixed Office Hours :
 +
  MTWR : 12:30pm-1:30pm
 +
 
 +
If you cannot meet during the previous office hours then please contact me to schedule another meeting time.
  
 
==Textbook Information==
 
==Textbook Information==
  
−
The bookstore sells an abridged version of the following text. The abridged version contains the seven chapters and an appendix:
+
    Textbook : [http://wps.aw.com/aw_lay_linearalg_updated_3/ Linear Algebra - David Lay, ISBN 0201824787]
  
−
1. Chapter 5: Power Series Solutions to ODE and [http://en.wikipedia.org/wiki/Frobenius_method Frobenius method]
+
=Course Documents=
 +
{{Start PDF Table}}
  
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2. Chapter 7: [http://en.wikipedia.org/wiki/Linear_algebra Systems of Linear Algebraic Equations]
+
==Syllabus ==
 +
{{PDF Table Item|filename=Math332_syllabus.summer2010.pdf | title=MATH332.Summer2010.Syllabus}}
  
−
3. Chapter 8: [http://en.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace Eigenvalues and Eigenvectors]
 
  
−
4. Chapter 11: [http://en.wikipedia.org/wiki/Fourier_series Fourier Series]
+
==Handouts==
  
−
5. Chapter 12: Introduction to Linear [http://en.wikipedia.org/wiki/Partial_differential_equation Partial Differential Equations]
+
{{PDF Table Item|filename=Math332_LAReview.summer2009.pdf|title= Linear Algebra Basics}}
 +
<!--{{PDF Table Item|filename=Math332_planes.summer2009.pdf|title= Three Planes in Space}}
 +
{{PDF Table Item|filename=Math332_LSP1.summer2009.pdf|title= Section 6.5.1 - Graph of Least Squares Problem from Class - The Blue Line is the LSP Soln}}
 +
{{PDF Table Item|filename=Math332_LSP2.summer2009.pdf|title= Section 6.5.1 - Graph of Least Squares Problem from Class - The Blue Line is the LSP Soln}}
 +
-->
  
−
6. Chapter 20: Numerical Methods in Linear Algebra
+
==Section Overviews==
  
−
7. Chapter 21: Numerical Methods in Differential Equations
+
The following is a set of documents providing an overview of each section of Lay's text that we cover. Listed in each set are:
  
−
8. Appendix A:
+
    Section  and pages from Lay's Linear Algebra
 +
    Suggested Problems from each section
 +
    Lecture Objectives
 +
    Lecture Goals 
  
−
While this will meet out needs, if you plan to continue in mathematics for a minor or area of special interest or seek an advanced degree in your field then you are advised to get the unabridged edition. Older editions are fine and relatively cheap from online retailers.
+
*[[MATH-332 Linear Algebra - Section Overview |MATH 332 : Linear Algebra - Section Overviews ]]
  
−
    Textbook : [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471488852.html Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9]
+
==Linear Algebra Slides==
−
    9th Edition Amazon : [http://www.amazon.com/Advanced-Engineering-Mathematics-Textbook-Solutions/dp/0470084847/ref=sr_1_4?ie=UTF8&s=books&qid=1231462860&sr=1-4 Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9]
+
−
    8th Edition Amazon (Used) : [http://www.amazon.com/gp/offer-listing/0471154962/ref=dp_olp_1 Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9]
+
  
−
=Course Materials=
+
*[[MATH-332 Linear Algebra - Slides |MATH 332 : Linear Algebra - Slides ]]
  
−
The following outlines materials specific to this course. The materials, as indicated, have been developed over time and have achieved a steady-state. An archive of [[MATH-348 Advanced Engineering Mathematics - Archive | older ticc pages ]] is available. There is also a binder available in the library of practically everything ever done since Fall 2006. The ticc websites pick up at Spring 2008 when I started presenting linear algebra first. 
 
  
−
==Syllabus==
+
==Assignments==
−
{{PDF Table Item|filename=Math348syllabus.pdf | title=MATH348.Syllabus}}
+
{{PDF Table Item|filename=Math332_hw0.e1.summer2010.pdf|title=MATH332.Summer2010.Homework0, Newest Posted at 8:44pm. If you did this already then don't worry.}}
 +
{{PDF Table Item|filename=Math332_hw1.summer2010.pdf|title=MATH332.Summer2010.Homework1}}
 +
{{PDF Table Item|filename=Math332_hw1.summer2010.soln.pdf|title=MATH332.Summer2010.Homework1-RowReductions}}
 +
{{PDF Table Item|filename=Math332_hw1.soln.summer2010.pdf|title=MATH332.Summer2010.Homework1 - Solutions}}
 +
{{PDF Table Item|filename=Math332_hw2.summer2010.pdf|title=MATH332.Summer2010.Homework2}}
 +
{{PDF Table Item|filename=Math332_hw2.soln.e1.summer2010.pdf|title=MATH332.Summer2010.Homework2 - Solutions : Correction to Problem 4 set 5, July 20th 8:30am}}
 +
Graphics for Homework 2
 +
      [http://ticc.mines.edu/csm/wiki/images/9/97/Math348_HW.1.2.1.Plot.pdf Geometry of Problem 3 System 1]
 +
      [http://ticc.mines.edu/csm/wiki/images/0/03/Math348_HW.1.2.2.Plot.pdf Geometry of Problem 3 System 2]
 +
      [http://ticc.mines.edu/csm/wiki/images/c/cc/Math348_HW.1.2.3.Plot.pdf Geometry of Problem 3 System 3]
 +
      [http://ticc.mines.edu/csm/wiki/images/c/cc/Math348_HW.1.2.4.Plot.pdf Geometry of Problem 3 System 4]
 +
      [http://ticc.mines.edu/csm/wiki/images/1/1d/Math348_HW.1.2.5.Plot.pdf Geometry of Problem 3 System 5]
 +
      [http://ticc.mines.edu/csm/wiki/images/c/ca/Math348_HW.1.4.2.1.Plot.pdf Interpolated Parabolas of Problem 5  Set 1]
 +
      [http://ticc.mines.edu/csm/wiki/images/a/a7/Math348_HW.1.4.2.2.Plot.pdf Interpolated Parabolas of Problem 5  Set 2]
 +
      [http://ticc.mines.edu/csm/wiki/images/a/a4/Math348_HW.1.4.2.2.lsp.Plot.pdf Geometry of Least Squares Problem of Problem 4  Set 2]
 +
      [http://ticc.mines.edu/csm/wiki/images/8/86/Math348_HW.1.4.2.3.Plot.pdf Interpolated Parabolas of Problem 5  Set 3]
  
−
==Lecture Slides==
 
  
−
There are various lecture slides associated with the course. They were developed during the Spring of 2010 and are intended to deliver important bulk concepts while avoiding the desire to write down 'every little thing.' Specifically, the slides address:
+
{{PDF Table Item|filename=Math332_hw3e2.summer2010.pdf|title=MATH332.Summer2010.Homework3 - Update 6:46am 7/12, minor(silly) typos corrected. Also, problem 4.7 and 4.8 somehow got intermixed and a negative sign was lost. They are separated now. }}
 +
{{PDF Table Item|filename=Math332_hw3.soln.summer2010.pdf|title=MATH332.Summer2010.Homework3 - Solutions}}
 +
{{PDF Table Item|filename=Math332_hw4.summer2010.pdf|title=MATH332.Summer2010.Homework4}}
 +
{{PDF Table Item|filename=Math332_hw4.soln.summer2010.pdf|title=MATH332.Summer2010.Homework4-Solutions}}
 +
{{PDF Table Item|filename=Math332_hw5.summer2010.pdf|title=MATH332.Summer2010.Homework5 : NOTE - I am not assuming that you start this before Monday. You can if you want but it is not necessary. Really, this was a tough week and you should take a break. However, if breaks just ain't your style or you can't take one then go ahead and give it a twirl.}}
 +
{{PDF Table Item|filename=Math332_hw5.soln.summer2010.pdf|title=MATH332.Summer2010.Homework5 - Solutions}}
 +
{{PDF Table Item|filename=Math332_hw6.summer2010.pdf|title=MATH332.Summer2010.Homework6}}
 +
{{PDF Table Item|filename=Math332_hw6.soln.summer2010.pdf|title=MATH332.Summer2010.Homework6-Solutions}}
 +
{{PDF Table Item|filename=Math332_hw7.summer2010.pdf|title=MATH332.Summer2010.Homework7}}
 +
{{PDF Table Item|filename=Math332_hw7.soln.summer2010.pdf|title=MATH332.Summer2010.Homework7 - Solutions : This PDF references the following assignments from Summer2009, which have mostly handwritten solutions.}} 
 +
 
 +
Start: Old Solutions Files Associated with Homework 7
 +
  {{PDF Table Item|filename=Math332_hw8.summer2009.pdf|title=MATH332.Summer2009.Homework8}}
 +
  {{PDF Table Item|filename=Math332_hw8a.soln.summer2009.pdf|title=MATH332.Summer2009.Homework8 - Solutions}}
 +
  {{PDF Table Item|filename=Math332_hw9.summer2009.pdf|title=MATH332.Summer2009.Homework9 - Extra Credit}}
 +
  {{PDF Table Item|filename=Math332_hw9a.soln.summer2009.pdf|title=MATH332.Summer2009.Homework9 - Solutions}}
 +
  End: Old Solutions Files Associated with Homework 7
  
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1. Definitions that are not useful for me to write and students to rewrite during lecture.
+
==Exams ==
  
−
2. Derivations that will never need to be reproduced but need to be communicated quickly because they lead to important consequences.
+
===Exam I===
 +
Exam I will be held on July 22nd in class. There will be no notecards or calculators. The exam will have five required questions and contain material from chapter 1-3. A good review would consist of revisiting your homework assignments and looking over the suggested problems outlined in the lecture slides. A good quick check of conceptual/linguistic understanding can be conducted through the true/false questions found in the problem set of every section.  
  
−
3. Derivations that will need to be reproduced and have been recorded for clarity.  
+
The following are quizzes and exams I have used in the past for this course. There are a few problems that are from material post-chapter3 please ignore these. They should be problems 3c,d, 4, 5 from exam 2.
  
−
Listed in each slide set are:
+
{{PDF Table Item|filename=Math332_exam1.summer2006.pdf|title=MATH332.Summer2006.Exam1}}
 +
{{PDF Table Item|filename=Math332_exam1.soln.summer2006.pdf|title=MATH332.Summer2006.Exam1-Solutions}}
 +
{{PDF Table Item|filename=Math332_exam2.summer2006.pdf|title=MATH332.Summer2006.Exam2}}
 +
{{PDF Table Item|filename=Math332_exam2.soln.summer2006.pdf|title=MATH332.Summer2006.Exam2-Solutions}}
 +
{{PDF Table Item|filename=Math332_quiz1.summer2006.pdf|title=MATH332.Summer2006.Quiz1}}
 +
{{PDF Table Item|filename=Math332_quiz1.soln.summer2006.pdf|title=MATH332.Summer2006.Quiz1-Solutions}}
 +
{{PDF Table Item|filename=Math332_Exam1a.Fall2008.pdf|title=MATH332.Fall2008}}
 +
{{PDF Table Item|filename=Math332_Exam1.soln.Fall2008.pdf|title=MATH332.Fall2008 - Solutions}}
  
−
    Associated Section/Pages from EK.AEM
 
−
    Associated Lecture Notes
 
−
    Associated Homework Assignments
 
  
−
*[[MATH-348 Advanced Engineering Mathematics - Lecture Slides |MATH 348 : Advanced Engineering Mathematics - Lecture Slides ]]
+
{{PDF Table Item|filename=Math332_exam1.summer2009.pdf|title=MATH332.Summer2009.Exam1}}
 +
{{PDF Table Item|filename=Math332_exam1.soln.summer2009.pdf|title=MATH332.Summer2009.Exam1-Solutions}}
  
−
==Lecture Notes==
 
  
−
There is a set of lecture notes associated with the course. They were developed during the Fall of 2008 through the Spring of 2009 and are intended to outline key-points, objectives and goals from the text in the order we cover them. Listed in each set are:
+
    Exam I - Statistics
 +
    Mean = xx
 +
    Median = xx
 +
    A's = xx, B's = xx, C's = xx, D's = xx, F's = xx, Total Number of Exams  = xx
  
−
    Associated Sections/Pages from EK.AEM
+
===Exam II ===
−
    Suggested Problems from EK.AEM
+
Exam II will be held on  August 11th in class. There will be no notecards or calculators. The exam will have five required questions and contain material from chapter 4-5. A good review would consist of revisiting your homework assignments and looking over the suggested problems outlined in the lecture slides. A good quick check of conceptual/linguistic understanding can be conducted through the true/false questions found in the problem set of every section.
−
    Brief Outline of Lecture Talking Points
+
−
    Lecture Objectives
+
−
    Lecture Goals 
+
  
−
*[[MATH-348 Advanced Engineering Mathematics - Lecture Notes |MATH 348 : Advanced Engineering Mathematics - Lecture Notes ]]
+
The following are quizzes and exams I have used in the past for this course. There are a few problems that are from material pre-chapter2 please ignore these.
  
−
==Assignments==
 
  
−
The assignments for this course have reached a steady-state. Consequently, solutions are often available through students who have taken the course in the past. Since these resources might not be available to all students, I have drafted a set of solutions to these homework assignments which I make available through this site. These solutions were, more or less, finalized during the Spring of 2010 and represents the end of an evolution starting around 2006. Outside of the lecture itself, these homeworks and solutions represents some of the oldest parts of the course and many of the ancestors can be found on [[MATH-348 Advanced Engineering Mathematics - Archive | older ticc pages ]].
+
{{PDF Table Item|filename=Math332_exam2.summer2006.pdf|title=MATH332.Summer2006.Exam2}}
 +
{{PDF Table Item|filename=Math332_exam2.soln.summer2006.pdf|title=MATH332.Summer2006.Exam2-Solutions}}
 +
{{PDF Table Item|filename=Math332_quiz2.summer2006.pdf|title=MATH332.Summer2006.Quiz2}}
 +
{{PDF Table Item|filename=Math332_quiz2.soln.summer2006.pdf|title=MATH332.Summer2006.Quiz2-Solutions}}
 +
{{PDF Table Item|filename=Math332_Exam2.Fall2008.pdf|title=MATH332.Fall2008 - Exam2}}
 +
{{PDF Table Item|filename=Math332_Exam2.soln.Fall2008.pdf|title=MATH332.Fall2008 - Exam2 -Solutions}}
 +
{{PDF Table Item|filename=Math332_Exam2.Summer2009.pdf|title=MATH332.Summer2009 - Exam2}}
 +
{{PDF Table Item|filename=Math332_Exam2.soln.Summer2009.pdf|title=MATH332.Summer2009 - Exam2 -Solutions}}
 +
 
 +
 
 +
    Exam II -  Statistics
 +
    Mean = x
 +
    Median = x
 +
    A's = x, B's = x, C's = x, D's = x, F's = x, Total Number of Exams  = x
 +
 
 +
{{PDF Table Item|filename=Math332_Exam2.Summer2010.pdf|title=MATH332.Summer2010 - Exam2}}
 +
{{PDF Table Item|filename=Math332_Exam2.soln.Summer2010.pdf|title=MATH332.Summer2010 - Exam2 -Solutions}}
 +
 
 +
===Final Exam===
 +
The Final Exam will be held on August 19th in class. There will be no notecards or calculators. The exam will have five questions, two will be from previous material, while the rest will contain material from chapter 6-7. A good review would consist of revisiting your homework assignments and looking over the suggested problems outlined in the lecture slides. A good quick check of conceptual/linguistic understanding can be conducted through the true/false questions found in the problem set of every section.  
 +
 
 +
A student should be prepared to handle the following concepts from previous material:
  
−
In the past the homeworks tended to have a good deal of discussion providing context to a problem so that both the mechanics and concepts could be gleaned. However, after talking with some students and course reviews I decided to move the commentary to the solutions in favor of a more streamlined problem statement. It is unclear whether this latest incarnation is 'better' than the past but what is clear is that they won't be regressing unless someone else wants to revamp them. If you want to see the previous versions then visit the [[MATH-348 Advanced Engineering Mathematics - Archive | older ticc pages ]]. If you find any typos in these solutions then I would appreciate you letting me know. They are pretty clean but they could always be `cleaner.'
+
1. Ax = b, solve the linear system and understand its geometric meaning
  
−
With that said, I must make emphasize the following point:
+
2. Linear Independence/Combination
−
      Caveat Emptor : We will work from these problems and since solutions are
+
−
      readily available it is up to the individual user to make sure that they
+
−
      are LEARNING the material. If you buy into a program of procrastination
+
−
      followed by rapid and thoughtless recreation then you may find an
+
−
      inadequate product, which cannot be returned.  
+
  
 +
3. Matrix Inversion and IMT
  
−
*[[MATH-348 Advanced Engineering Mathematics - Assignments |MATH 348 : Advanced Engineering Mathematics - Assignments ]]
+
4. Rank and Nullity
  
−
==Exams==
+
5. Eigenvalues/Eigenvectors Diagonalization
  
 +
The following are quizzes and exams I have used in the past for this course. There will be no exam from Fall2008 since this material would have been found on a final exam and it is departmental policy to not let that cat out of its box.
  
−
*[[MATH-348 Advanced Engineering Mathematics - Exams |MATH 348 : Advanced Engineering Mathematics - Exams ]]
+
{{PDF Table Item|filename=Math332_exam3.summer2006.pdf|title=MATH332.Summer2006.Exam3}}
 +
{{PDF Table Item|filename=Math332_exam3.soln.summer2006.pdf|title=MATH332.Summer2006.Exam3-Solutions}}
 +
{{PDF Table Item|filename=Math332_quiz3.summer2006.pdf|title=MATH332.Summer2006.Quiz3}}
 +
{{PDF Table Item|filename=Math332_quiz3.soln.summer2006.pdf|title=MATH332.Summer2006.Quiz3-Solutions}}
  
−
=Supplemental Materials=
+
==Course Links==
  
−
*[[MATH-348 Advanced Engineering Mathematics - Supplemental  |MATH 348 : Advanced Engineering Mathematics - Supplemental Materials ]]
+
===Matrix Algebra===
−
*[[MATH-348 Advanced Engineering Mathematics - Archive |MATH 348 : Advanced Engineering Mathematics - Archive ]]
+
    [http://www.purplemath.com/modules/mtrxmult.htm Scalar and Matrix Multiplication with Animations]
 +
    [http://www.mathresource.iitb.ac.in/linear%20algebra/example2.0.2/index.html Animated Matrix Multiplication]
 +
    [http://www.sci.wsu.edu/math/faculty/genz/220v/lessons/kentler/FullMult/fullMatrixMultiply.html Animated Matrix Multiplication]
 +
===Computational Tools===
 +
    [http://eigenmath.net/ Free Mathematica Like Program for Windows and Mac]
 +
    [http://eigenmath.net/Eigenmath.pdf Eigenmath Manual]

Latest revision as of 03:24, 19 August 2010

Main Page > Mathematical and Computer Sciences Course Wikis

Contents

Course Information

MATH332: Linear Algebra - Systems of linear equations, matrices, determinants and eigenvalues. Linear operators. Abstract vector spaces. Applications selected from linear programming, physics, graph theory, and other fields. Prerequisite: MATH 213, 223 or 224.

Instructor Information

Instructor : Scott Strong

Office : Chauvenet Hall 266

Office Phone : 303.384.2446

email : math332.summer2010@gmail.com

Course Calendar

Classes Begin : June 28th, 2010

Meeting Days : Monday, Tuesday, Wednesday, Thursday

Course Sections : 

    Section A,  3:00pm-4:20pm, Green Center 249


Classes End : August 19th, 2009

Important Dates : 

   July 5th - No Class 
   July  6th - Last Day to Withdrawal  (Without a W)
   August 6th - Last Day to Withdrawal

Office Hours

Fixed Office Hours : 

 MTWR : 12:30pm-1:30pm

If you cannot meet during the previous office hours then please contact me to schedule another meeting time.

Textbook Information

    Textbook : Linear Algebra - David Lay, ISBN 0201824787

Course Documents

Pdf.png These downloads require Adobe Acrobat Reader

Syllabus

MATH332.Summer2010.Syllabus


Handouts

Linear Algebra Basics

Section Overviews

The following is a set of documents providing an overview of each section of Lay's text that we cover. Listed in each set are: 

   Section  and pages from Lay's Linear Algebra
   Suggested Problems from each section
   Lecture Objectives
   Lecture Goals

Linear Algebra Slides


Assignments

MATH332.Summer2010.Homework0, Newest Posted at 8:44pm. If you did this already then don't worry.
MATH332.Summer2010.Homework1
MATH332.Summer2010.Homework1-RowReductions
MATH332.Summer2010.Homework1 - Solutions
MATH332.Summer2010.Homework2
MATH332.Summer2010.Homework2 - Solutions : Correction to Problem 4 set 5, July 20th 8:30am 
Graphics for Homework 2
     Geometry of Problem 3 System 1
     Geometry of Problem 3 System 2
     Geometry of Problem 3 System 3
     Geometry of Problem 3 System 4
     Geometry of Problem 3 System 5
     Interpolated Parabolas of Problem 5  Set 1
     Interpolated Parabolas of Problem 5  Set 2
     Geometry of Least Squares Problem of Problem 4  Set 2
     Interpolated Parabolas of Problem 5  Set 3


MATH332.Summer2010.Homework3 - Update 6:46am 7/12, minor(silly) typos corrected. Also, problem 4.7 and 4.8 somehow got intermixed and a negative sign was lost. They are separated now.
MATH332.Summer2010.Homework3 - Solutions
MATH332.Summer2010.Homework4
MATH332.Summer2010.Homework4-Solutions
MATH332.Summer2010.Homework5 : NOTE - I am not assuming that you start this before Monday. You can if you want but it is not necessary. Really, this was a tough week and you should take a break. However, if breaks just ain't your style or you can't take one then go ahead and give it a twirl.
MATH332.Summer2010.Homework5 - Solutions
MATH332.Summer2010.Homework6
MATH332.Summer2010.Homework6-Solutions
MATH332.Summer2010.Homework7
MATH332.Summer2010.Homework7 - Solutions : This PDF references the following assignments from Summer2009, which have mostly handwritten solutions. 
Start: Old Solutions Files Associated with Homework 7
MATH332.Summer2009.Homework8
MATH332.Summer2009.Homework8 - Solutions
MATH332.Summer2009.Homework9 - Extra Credit
MATH332.Summer2009.Homework9 - Solutions 
 End: Old Solutions Files Associated with Homework 7

Exams

Exam I

Exam I will be held on July 22nd in class. There will be no notecards or calculators. The exam will have five required questions and contain material from chapter 1-3. A good review would consist of revisiting your homework assignments and looking over the suggested problems outlined in the lecture slides. A good quick check of conceptual/linguistic understanding can be conducted through the true/false questions found in the problem set of every section.

The following are quizzes and exams I have used in the past for this course. There are a few problems that are from material post-chapter3 please ignore these. They should be problems 3c,d, 4, 5 from exam 2.

MATH332.Summer2006.Exam1
MATH332.Summer2006.Exam1-Solutions
MATH332.Summer2006.Exam2
MATH332.Summer2006.Exam2-Solutions
MATH332.Summer2006.Quiz1
MATH332.Summer2006.Quiz1-Solutions
MATH332.Fall2008
MATH332.Fall2008 - Solutions


MATH332.Summer2009.Exam1
MATH332.Summer2009.Exam1-Solutions 


    Exam I -  Statistics
    Mean = xx
    Median = xx
    A's = xx, B's = xx, C's = xx, D's = xx, F's = xx, Total Number of Exams  = xx

Exam II

Exam II will be held on August 11th in class. There will be no notecards or calculators. The exam will have five required questions and contain material from chapter 4-5. A good review would consist of revisiting your homework assignments and looking over the suggested problems outlined in the lecture slides. A good quick check of conceptual/linguistic understanding can be conducted through the true/false questions found in the problem set of every section.

The following are quizzes and exams I have used in the past for this course. There are a few problems that are from material pre-chapter2 please ignore these.


MATH332.Summer2006.Exam2
MATH332.Summer2006.Exam2-Solutions
MATH332.Summer2006.Quiz2
MATH332.Summer2006.Quiz2-Solutions
MATH332.Fall2008 - Exam2
MATH332.Fall2008 - Exam2 -Solutions
MATH332.Summer2009 - Exam2
MATH332.Summer2009 - Exam2 -Solutions 


    Exam II -  Statistics
    Mean = x
    Median = x
    A's = x, B's = x, C's = x, D's = x, F's = x, Total Number of Exams  = x
MATH332.Summer2010 - Exam2
MATH332.Summer2010 - Exam2 -Solutions

Final Exam

The Final Exam will be held on August 19th in class. There will be no notecards or calculators. The exam will have five questions, two will be from previous material, while the rest will contain material from chapter 6-7. A good review would consist of revisiting your homework assignments and looking over the suggested problems outlined in the lecture slides. A good quick check of conceptual/linguistic understanding can be conducted through the true/false questions found in the problem set of every section.

A student should be prepared to handle the following concepts from previous material:

1. Ax = b, solve the linear system and understand its geometric meaning

2. Linear Independence/Combination

3. Matrix Inversion and IMT

4. Rank and Nullity

5. Eigenvalues/Eigenvectors Diagonalization

The following are quizzes and exams I have used in the past for this course. There will be no exam from Fall2008 since this material would have been found on a final exam and it is departmental policy to not let that cat out of its box.

MATH332.Summer2006.Exam3
MATH332.Summer2006.Exam3-Solutions
MATH332.Summer2006.Quiz3
MATH332.Summer2006.Quiz3-Solutions

Course Links

Matrix Algebra

   Scalar and Matrix Multiplication with Animations
   Animated Matrix Multiplication
   Animated Matrix Multiplication

Computational Tools

   Free Mathematica Like Program for Windows and Mac
   Eigenmath Manual
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