assignments
Current Reading: Three.VI on projections and to the end of Four, on determinants (but don't worry too much about all the different methods for calculating determinants, just make sure you can do it reasonably efficiently).
due Fri Sep 17
Assignment 1
- From One.I : 1.22, 1.33, 2.30, 3.16.
- From One.II: 1.5, 2.14, 2.33.
- From One.III: 2.18.
due Thu Sep 23
Project 1
Group work on one of the three "topics" at the end of Chapter 1. Present your work in class on 23rd September.
due Fri Oct 1
Assignment 2
- From Two.I : 1.24, 1.25, 1.26, 1.31, 2.27, 2.42, 2.45.
- From Two.II: 1.28, 1.29, 1.38
due Fri Oct 8
Assignment 3
Find the error in the "proof" of this "theorem":
Theorem. All horses are the same color.
Proof. We prove the statement "Given any set of n horses, all n horses are the same color".
Base Case: Given a set with just one horse, the one horse has a color. All the horses in that set are that color and the base case is proven.
Induction Hypothesis: Assume that given any set of k horses, the horses are all the same color.
Induction Step. Take any set of k+1 horses and put them in an arbitrary order h1,h2,...,hk + 1
. By the induction hypothesis the horses h1,h2,...,hk
are the same color. Similarly, by the induction hypothesis the horses h2,h3,...,hk + 1
are the same color. So all k+1 horses are the same color.
Conclusion. By induction, given any set of n horses, the horses are all the same color. As the number of horses is finite, all horses are the same color. QED.
Note: the idea is not to show the result is false (i.e. don't bring a counterexample to class; they'll make a mess) but to find the flaw in the reasoning.
- From Two.III: 1.18, 1.28, 2.15, 2.29, 2.34, 3.16, 3.19, 3.29.
due Tue Oct 12
Project 2
Group work on one of the topics at the end of Chapter 2. Present your work in class on 8th October.
due Thu Oct 14
Quiz 1
due Fri Oct 29
Assignment 4
- Three.I: 1.28
- Three.II: 1.25, 1.38, 2.27
- Three.III: 1.12, 1.15, 1.21, 2.19
- Three.IV: 1.13, 2.15, 2.25, 2.29, 3.38, 4.16d, 4.16e, 4.16f
- Three.V: 1.6, 1.15
due Tue Nov 9
Project 3
Individial work on one of the topics at the end of Chapter 3 or 4. Lots will be drawn for topics on 2nd November (you may trade).
due Thu Nov 11
Quiz 2
Covering Chapters 3 and 4.
due Fri Nov 12
Assignment 5
- Three.VI: 1.9, 1.12, 2.9a, 2.10a,
- Four.I: 2.8, 2.13, 3.24,
- Four.II: 1.8, 1.24, 1.29
due Mon Nov 29
Assignment 6
- Five.II: 1.10, 1.14, 2.18, 3.20a, 3.22, 3.40,
- Five.III: 1.14, 2.19, 2.25,
- Five.IV: 1.24, 2.21b, 2.21c.
due Thu Dec 9
Quiz 3
due Tue Dec 14
Final Exam
I'll email this out and put hardcopies in my envelope by 10am on Monday.
Final Grade
(Placeholder title so that it appears in the grade page.)
