BU CAS MA 142 Spr 2013

Mathematics 142 - Introduction to Linear Algebra

lectures:
   Tue. & Thu., 3:30 PM - 5:00 PM in MCS B23
   lecturer: Andrei Lapets (lapets@bu.edu, MCS 176)
   OH: Tue. 1-3 PM; Wed. 3-4 PM
for questions and discussion:
casma142a1-l@bu.edu (course mailing list)
Q&A page on Piazza

homework assignment policies:
   submission: by 11:59 PM on due date (by email)
   collaboration: discussion only; list all collaborators
   late policy: -10 points per day, 5 days maximum

course grade:
50% homework + 50% max{final, avg{mid, final}}

course materials:
   lecture notes (with assignments and review problems)
   assignment #1
   assignment #2
   assignment #3
   assignment #4
   assignment #5
   practice final (with solutions)

other reading materials (not required):

   Linear Algebra with Applications.
     Otto Bretscher.

   Linear Algebra and Its Applications.
     David C. Lay.

academic conduct code

2013-01-17	lecture: introduction & motivation	course organization lecture notes high-level overview of course material models, systems, and system states review of algebra of real numbers vectors and vector addition related readings: [Lay 2012]: 1.1; 1.3
2013-01-22	lecture: vectors	lecture notes more about algebraic properties more review of logical formulas vector addition & scalar multiplication vector norms and dot products in R² linear dependence and independence orthogonality of vectors related readings: [Lay 2012]: 6.1; 6.2 [Bretscher 2009]: 1.3.6; 5.1; A.4
2013-01-24	lecture: vectors	lecture notes properties of equality more proof examples and strategies projections of vectors onto vectors vector negation and subtraction related readings: [Lay 2012]: 6.1; 6.2 [Bretscher 2009]: 2.2; 5.1; 5.5.2
2013-01-29	lecture: vectors	lecture notes review of orthogonal projections lines (as sets of vectors) vector equations and y = mx + b linear combinations of vectors related readings: [Lay 2012]: 6.1 [Bretscher 2009]: 2.2
2013-01-31	lecture: vectors	lecture notes lines and planes (as sets of vectors) more practice with vector properties linear combinations in applications related readings: [Lay 2012]: 1.10; 6.1 [Bretscher 2009]: 2.2
2013-02-04		assignment #1 due
2013-02-05	lecture: matrices	lecture notes linear combinations in applications from linear combinations to matrices interpretations of matrices matrix operations and properties related readings: [Lay 2012]: 1.6; 1.10; 2.1
2013-02-07	lecture: matrices	lecture notes review: maps and composition matrix multiplication derived dimension relationships system states over time some subsets of R^n×n and properties identity matrix scalar matrices diaigonal matrices related readings: [Lay 2012]: 1.10; 2.1 [Bretscher 2009]: 2.1; 2.3
2013-02-12	lecture: matrices	lecture notes invertible matrices determinant & inverse of R^2×2 matrix related readings: [Lay 2012]: 2.1; 2.2; 2.3 [Bretscher 2009]: 2.1; 2.3; 2.4
2013-02-14	lecture: matrices	lecture notes more subsets of R^n×n and properties upper triangular matrices lower triangular matrices Mv = w for M with various properties elementary matrices & row operations reduced row echelon forms of matrices related readings: [Lay 2012]: 1.2; 2.3; 2.5 [Bretscher 2009]: 1.2; 1.3; 2.4
2013-02-15		assignment #2 due
2013-02-19	lecture: matrices	lecture notes elementary matrices & row operations more facts about invertible matrices matrix PLU factorization related readings: [Lay 2012]: 1.2; 2.3; 2.5 [Bretscher 2009]: 1.2; 1.3; 2.4
2013-02-21	lecture: matrices	lecture notes more on rref & row operations basic example from physics orthogonal matrices and rotations related readings: [Lay 2012]: 1.2; 2.3; 2.5 [Bretscher 2009]: 1.2; 1.3; 2.4
2013-02-26	lecture: matrices & vector spaces	lecture notes orthogonal matrices and rotations matrix rank introduction to vector spaces sets of vectors and their notation
2013-02-28	lecture: review	lecture notes
2013-03-01		assignment #3 due
2013-03-05 Tuesday 3:30-5 PM	midterm exam
2013-03-07	lecture: vector spaces	review of midterm problems lecture notes spans of vectors equality of spans
2013-03-12	spring recess
2013-03-14	spring recess
2013-03-19	lecture: vector spaces	lecture notes sets of vectors span notation for sets of vectors membership in spans equality of spans related readings: [Lay 2012]: 4.1; 4.3 [Bretscher 2009]: 3.1.2; 3.2; 4.1
2013-03-21	lecture: vector spaces	lecture notes abstract vector spaces sets of polynomials as vector spaces fitting polynomials to points in R² related readings: [Bretscher 2009]: 4.1
2013-03-26	lecture: vector spaces	lecture notes sets of polynomials as vector spaces fitting polynomials to points in R² basis and dimension of a vector space related readings: [Lay 2012]: 4.3; 4.5 [Bretscher 2009]: 3.2; 3.3; 4.1
2013-03-28	lecture: vector spaces	lecture notes basis and dimension of a vector space orthonormal basis of a vector space Gram-Schmidt process related readings: [Lay 2012]: 4.3; 4.5; 6.2; 6.4 [Bretscher 2009]: 3.2; 3.3; 5.1; 5.2
2013-04-02	lecture: vector spaces	lecture notes projection onto a vector subspace over- & underdetermined systems homogenous & non-homogenous systems least-squares approximations related readings: [Lay 2012]: 1.5; 6.2; 6.3 [Bretscher 2009]: 3.1.2; 3.2; 4.1
2013-04-04	lecture: vector spaces	lecture notes least-squares curve fitting applications of curve fitting approximating system relationships related readings: [Lay 2012]: 6.5; 6.6; 8.1 [Bretscher 2009]: 5.4
2013-04-09	lecture: linear transformations	lecture notes distributed computation of least-squares intersections & products of vector spaces product spaces, relations, & maps
2013-04-11	lecture: linear transformations	lecture notes linear transformations & examples injections & surjections bijections & isomorphisms related readings: [Lay 2012]: 1.9; 2.9.1; 4.4.5 [Bretscher 2009]: 3.1; 3.2; 4.2
2013-04-12		assignment #4 due
2013-04-16	lecture: linear transformations	lecture notes projection as a linear transformation bijections & isomorphisms matrices as linear transformations related readings: [Lay 2012]: 1.9; 2.9.1; 4.4.5 [Bretscher 2009]: 3.1; 3.2; 4.2; 5.4
2013-04-18	monday schedule
2013-04-23	lecture: applications to linear systems	lecture notes affine spaces applications in communications related readings: [Lay 2012]: 8.1
2013-04-25	lecture: eigenvectors & eigenvalues	lecture notes fixed points and spaces eigenvectors and eigenvalues related readings: [Lay 2012]: 5.1; 5.2; 5.4 [Bretscher 2009]: 7.1; 7.2; 7.3
2013-04-30	lecture: review	lecture notes
2013-05-02	lecture: review	lecture notes
2013-05-03		assignment #5 due
2013-05-09 Thursday 3-5 PM MCS B23	final exam