MTH5102 Linear Algebra Spring 2017 Syllabus Instructor: Dr. Aaron Welters; O¢ ce: Crawford Bldg., Room 319; Phone: (321) 674-7202; Email:
[email protected] O¢ ce hours: Mon. & Wed. 5pm-7pm, and by appointment. Course webpage: http://www.fit.edu/~awelters/Teaching/2017/Spring/MTH 5102.html Course description: MTH5102 (3 credits) – Linear algebra, systems of linear equations and Gauss elimination method; inverses, rank and determinants; vector spaces; linear transformations, linear functional and dual spaces; eigenvalues, eigenvectors; symmetric, Hermitian and normal transformations; and quadratic forms. (Requirement: Undergraduate course in multivariable calculus or linear algebra.) Lecture time: Mon. and Wed. at 7pm-8:15pm in Crawford Bldg., Room 112. The course will run from Jan. 9, 2017 to May 5, 2017 & the last day of classes is Apr. 26, 2016. The …nal exam is on Wednesday, May 3 at 6pm-8pm in Crawford Bldg., Room 112. We have in total 26 days of lectures and 3 days of exams. The last day of Spring classes is Wed. 04/26; the …rst day of Spring classes is Mon. 01/09. Breaks and holidays are: 01/16 Mon.; 02/20 Mon.; 03/06-03/10 Mon.-Fri.; Study Days (no classes) are: 04/27 Thur. & 04/28 Fri. Course textbook: [FIS02] S. H. Friedberg, A. J. Insel, and L. E. Spence. Linear Algebra. 4th Ed., Pearson, 2002. Reference books: [GS06] Strang, G. Linear Algebra and its Applications. 4th Ed., Brooks Cole, 2006. [PL07] Lax, P. Linear Algebra and its Applications. 2nd Ed., John Wiley & Sons, Inc., 2007. [LT07] Lancaster, P. and Tismenetsky, M. The Theory of Matrices. 2nd Ed., Academic Press, 1985. [SR08] Roman, S. Advanced Linear Algebra. 3rd Ed., Springer, 2008. [PH87] Halmos, P. Finite-Dimensional Vector Spaces. Springer, 1987. Exams: There will be 3 exams the last of which is a comprehensive …nal exam. The …rst two exams are scheduled for 02/8 and 03/27, 7pm-8:15pm, Crawford Bldg., Room 112. The …nal exam is 05/03, 6pm-8pm, Crawford Bldg., Room 112. Homework: Homework will consist of weekly problem sets which will be posted on the course webpage each Wed. by 11:59pm and due the following Wed. by end of class. Late problem sets are not accepted. Additionally, extra credit problem sets will occasionally be given out which can improve your homework scores. Grading Policy: Your grade will be based on 20% prob. sets + 40% midterms (20% each) + 40% …nal. Your …nal grade will be determined by your homework (including extra credit) after dropping your lowest homework score. 1
Drop dates: 01/20 –last day to drop class with full tuition refund & without receiving a grade of W; 03/17 –Last day to withdraw from class with a …nal grade of W. Last day of classes: 04/26 The small print Collaboration policy: Independently of whether you collaborate or not, any homework submitted must be formulated by you in your own words. Word-by-word copying is strictly forbidden, and may result in a 0 point score for all concerned. Missed homeworks: If you have to miss a homework deadline for some valid reason, contact the lecturer. An attempt will then be made to deal with the matter satisfactorily. The arrangement will be con…rmed by email to you, which you should keep for your records. Do not count on anyone else to make such arrangements for you: you’re in charge of getting things done. All such matters must be resolved before the last day of classes: no further changes to homework scores will be made after that. The same applies to midterm scores. Exams: Closed book, no notes allowed, and NO electronic devices will be allowed in the exams. Finally: The material covered in this class is great, make sure you stay on top of it and you will do very well !
Monday
Tuesday Wednesday
1/9
1/11
1/10
1.1 Intro.
Thursday Friday 1/12
1/13
1/19
1/20
1/26
1/27
2/2
2/3
2/9
2/10
2/16
2/17
2/23
2/24
3/2
3/3
3/9
3/10
3/16
3/17
3/23
3/24
3/30
3/31
4/6
4/7
4/13
4/14
4/20
4/21
4/27
4/28
5/4
5/5
1.2 Vec. Spaces
1.2 Vec. Spaces
1/16
1.3 Subpaces
1/18
1/17
Holiday
1.4 Sys. of Linear Eqs.
No Class
1.5 Linear Indep.
1/23
1/24
1.5 Linear Indep.
1/25 1.6 Bases & Dim .
1.6 Bases & Dim .
1/30
2/1
1/31
2.2 M atrix Reprs.
2.1 Linear Trans., Ker. & Ran.
2.3 Com p. & M ult.
2/6
2/7
2/8
2.3 Com p. & M ult.
M idterm
2.4 Inv. & Isom .
Exam 1
2/13
2/15
2/14
2.4 Inv. & Isom .
2.5 Change of Co ord.
2.5 Change of Co ord.
2.6 Dual Spaces
2/20
2/22
2/21
Holiday
3.1 Elem . Ops. & M atr.
No Class
3.2 M atrix Rank & Inv.
2/27
3.3 Sys. of Linear Eq.
3.3 Sys. of Linear Eq.
3/6
3/1
2/28
3.2 M atrix Rank & Inv.
3.4 Sys. of Linear Eq.
3/7
Spring Break
3/8 Spring Break
No Class
No Class
3/13
3/14
3.4 Sys. of Linear Eq.
3/15 4.2 Det. of order n
4.1 Det. of order 2
3/20
3/21
4.3 Prop. of Det.
3/27
3/22 5.1 Eigenvalues & Eigenvec.
3/28
M idterm
3/29 5.2 Diagonalizability
Exam 2
4/3
4/5
4/4
6.1 Inner Pro ducts & Norm s
5.4 Cayley-Ham ilton Thm
6.2 G ram -Schm idt O rthog.
4/10
4/11
6.2 G ram -Schm idt O rthog.
4/12 6.4 Norm al & Self-Adj. Ops.
6.3 Adjoint Op.
4/17
4/18
6.5 Unitary O ps.
4/24
4/19 6.6 Sp ectral Thm .
4/25
6.7 Sing. Val. Decom p.
4/26 6.8 Quadratic Form s
6.8 Q uadratic Form s
5/1
5/2
5/3
Finals
Final
Week
Exam
