MATH 1200 Algebra
Welcome to the homepage of Math 1200 (Algebra). This page contains
general information relating to the Algebra course in Math 1200 (First Science
Mathematics General) at UCD, as well as detailed course materials
relating to the
academic year 2004-2005. These are also available at the Math
1200 Blackboard Site, which can be accessed by UCD students
through
http://elearning.ucd.ie.
Contents
Lecturer
News
Syllabus
Study Advice
Course Notes
Homework
Dr Rachel Quinlan
Office : Room 6, Mathematics Department, Science Lecture Building (Second Floor)
Phone : (716) 2548
email : rachel.quinlan@ucd.ie
- Lectures in the 2004-2005 academic year will begin on Thursday
September 16.
- Current course materials can be found on the Math 1200 Blackboard
site.
Chapter 1 Systems of Linear Equations
Chapter 2 Matrix Arithmetic
Chapter 3 Square matrices : Inverses and Determinants
Chapter 4 Introduction to Vector Geometry
Chapter 5 Vectors in R3
Chapter 6 Eigenvalues and Eigenvectors
The course notes should be sufficient as a "text" for this course. For supplementary reading I recommend Anton's "Elementary Linear Algebra", which is published by Wiley. This textbook includes a comprehensive treatment of all topics on the Math 1200 (Algebra) syllabus and plenty of practice problems.
- It is important to read the course notes carefully and to make sure that you have a good understanding of the central ideas. This may not be an instantaneous process - you may have to revisit some of the themes many times before you are completely comfortable with them. You shouldn't be discouraged by this, remember that the subject we are studying was not developed overnight, but rather over centuries of concentrated effort.
- It is essential to work through plenty of practice problems in linear algebra. Techniques such as reducing a matrix to row-echelon form, finding the equation of a plane, matrix multiplication, computing inverses and determinants of matrices, computing characteristic polynomials, etc., can only be perfected through practice. It is essential to acquire confidence and dexterity with these techniques : use the examples in the course notes as guidelines, but don't rely solely on them, make sure that you practise similar examples yourself.
Practice problems can be found in the First Year Problem Book, in Anton's "Elementary Linear Algebra" or indeed in any introductory textbook on linear algebra, of which numerous examples can be found in the library.
- Feel free to contact me about any questions you might have,
either in person at my office or after class, or by phone or email.
Outline course notes are available below in .pdf format. These notes
are for the 2004/05 academic year.
The purpose of these notes, if you choose to use them, is to relieve
you of the need to write long passages of material during class. They
are not intended to relieve you of the need to attend class!
In some cases examples (in the online notes) are different from the
corresponding examples in the (in-class) lecture notes, although
completely equivalent
in terms of the methods and ideas they involve. In some of these cases
you may find it helpful to have more than one worked example on hand.
Chapter 1
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Chapter 2
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Chapter 3
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Chapter 4
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Chapter 5
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Chapter 6
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The notes from the 2003/04 academic year are below. These may be of
interest to students who are repeating the course externally this year.
Chapter 1
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Chapter 2
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Chapter 3
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Chapter 4
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Chapter 5
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Chapter 6
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Chapter 7
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Chapter 8
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Homework problems will be posted here as well as at the Blackboard
site as we progress through the year. Note the odd-numbered homework
assignments are in calculus - Homework 2 is the first algebra
homework.
1. Homework 2 - posted 4/10/04, on systems
of linear equations.
Solutions to Homework 2
2. Homework 4 - posted 15/10/04, on matrix multiplication.
Solutions to Homework 4
3. Homework 6 - posted 29/10/04, on matrix
inverses.
Solutions to Homework 6
4. Homework 8 - posted 12/11/04, on
3 by 3 matrix inverses.
Solutions to Homework 8
5. Homework 10 - posted 29/11/04, on
vectors in R2.
Solutions to Homework 10
6. Homework 12 - posted 17/01/05, on
vectors in R2.
Solutions to Homework 12
7. Homework 14 - posted 28/01/05, on
equations of planes.
Solutions to Homework 14
8. Homework 16 - posted 14/02/05, on
cross products and vector equations of lines.
Solutions to Homework 16
9. Homework 18 - posted 7/03/05, on
eigenvalues and eigenvectors.
Solutions to Homework 18
Note The picture at the top of this page is from an Albanian stamp honouring
René Descartes, one of the originators of coordinate geometry. For more stamps featuring mathematicians, see
this site.
UCD Blackboard login
MATH1200 homepage
MATH1200 Calculus
UCD Department of Mathematics
Faculty of Science