Welcome to Math 240! (additions to this web site no longer count towards good deed points)

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Week of...

Notes and Links

1

Sep 8

About This Class, What is this class about? (PDF, HTML), Monday, Wednesday

2

Sep 15

HW1, Monday, Wednesday, TheComplexField.pdf,HW1_solutions.pdf

3

Sep 22

HW2, Class Photo, Monday, Wednesday, HW2_solutions.pdf

4

Sep 29

HW3, Wednesday, Tutorial, HW3_solutions.pdf

5

Oct 6

HW4, Monday, Wednesday, Tutorial, HW4_solutions.pdf

6

Oct 13

No Monday class (Thanksgiving), Wednesday, Tutorial

7

Oct 20

HW5, Term Test at tutorials on Tuesday, Wednesday

8

Oct 27

HW6, Monday, Why LinAlg?, Wednesday, Tutorial

9

Nov 3

Monday is the last day to drop this class, HW7, Monday, Wednesday, Tutorial

10

Nov 10

HW8, Monday, Tutorial

11

Nov 17

MondayTuesday is UofT November break

12

Nov 24

HW9

13

Dec 1

Wednesday is a "makeup Monday"! EndofCourse Schedule, Tutorial

F

Dec 8

The Final Exam

Register of Good Deeds

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This assignment is due at the tutorials on Tuesday September 23. Here and everywhere, neatness counts!! You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.
Read appendices A through D in our textbook (with higher attention to C and D), and solve the following problems:
 Suppose $a$ and $b$ are nonzero elements of a field $F$. Using only the field axioms, prove that $a^{1}b^{1}$ is a multiplicative inverse of $ab$. State which axioms are used in your proof.
 Prove that if $a$ and $b$ are elements of a field $F$, then $a^{2}=b^{2}$ if and only if $a=b$ or $a=b$.
 Let $F_{4}=\{0,1,a,b\}$ be a field containing 4 elements. Assume that $1+1=0$. Prove that $b=a^{1}=a^{2}=a+1$. (Hint: For example, for the first equality, show that $a\cdot b$ cannot equal $0$, $a$, or $b$.)
 Write the following complex numbers in the form $a+ib$, with $a,b\in {\mathbb {R} }$:
 ${\frac {1}{2i}}+{\frac {2i}{5i}}$.
 $(1+i)^{5}$.

 Prove that the set $F_{1}=\{a+b{\sqrt {3}}:a,b\in {\mathbb {Q} }\}$ (endowed with the addition and multiplication inherited from ${\mathbb {R} }$) is a field.
 Is the set $F_{2}=\{a+b{\sqrt {3}}:a,b\in {\mathbb {Z} }\}$ (with the same addition and multiplication) also a field?
Scanned Assignment Solutions by Boyang.wu
File:A11.pdf
File:A12.pdf