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people:fer:330ws:fall2018:homework

Math 330 - 03 Homework (Fall 2018)

  • LaTeX-ed solutions are encouraged and appreciated.
  • If you use LaTeX, hand-in a printed version of your homework.
  • You are encouraged to discuss homework problems with classmates, but such discussions should NOT include the exchange of any written material.
  • Writing of homework problems should be done on an individual basis.
  • References to results from the textbook and/or class notes should be included.
  • The following lists should be considered partial and tentative lists until the word complete appears next to it.
  • Use 8.5in x 11in paper with smooth borders. Write your name on top of each page. Staple all pages.

$\newcommand{\aut}{\textrm{Aut}} \newcommand{\sub}{\textrm{Sub}} \newcommand{\join}{\vee} \newcommand{\bigjoin}{\bigvee} \newcommand{\meet}{\wedge} \newcommand{\bigmeet}{\bigwedge} \newcommand{\normaleq}{\unlhd} \newcommand{\normal}{\lhd} \newcommand{\union}{\cup} \newcommand{\intersection}{\cap} \newcommand{\bigunion}{\bigcup} \newcommand{\bigintersection}{\bigcap} \newcommand{\sq}[2][\ ]{\sqrt[#1]{#2\,}} \newcommand{\pbr}[1]{\langle #1\rangle} \newcommand{\ds}{\displaystyle} \newcommand{\C}{\mathbb{C}} \newcommand{\R}{\mathbb{R}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\N}{\mathbb{N}} \newcommand{\A}{\mathbb{A}} \newcommand{\F}{\mathbb{F}} \newcommand{\T}{\mathbb{T}} \newcommand{\ol}[1]{\overline{#1}} \newcommand{\imp}{\Rightarrow} \newcommand{\rimp}{\Leftarrow} \newcommand{\pinfty}{1/p^\infty} \newcommand{\power}{\mathcal{P}} \newcommand{\calL}{\mathcal{L}} \newcommand{\calC}{\mathcal{C}} \newcommand{\calN}{\mathcal{N}} \newcommand{\calB}{\mathcal{B}} \newcommand{\calF}{\mathcal{F}} \newcommand{\calR}{\mathcal{R}} \newcommand{\calS}{\mathcal{S}} \newcommand{\calU}{\mathcal{U}} \newcommand{\calT}{\mathcal{T}} \newcommand{\gal}{\textrm{Gal}} \newcommand{\isom}{\approx} \newcommand{\glb}{\textrm{glb}} $

Problem Set 12 (complete) Due: 11/19/2018. Board presentation: 11/??/2018

  1. Prove Prop. 10.17
  2. Prove Prop. 10.23.iii

Problem Set 11 (complete) Due: 11/12/2018. Board presentation: 11/16/2018

  1. Prove the following corollary to Prop. 10.4
    Corollary: $\glb(\R^+)=0$.
  2. Prove Prop. 10.7
  3. Prove Prop. 10.10.iii
  4. Prove Prop. 10.13.ii

Problem Set 10 (complete) Due: 11/05/2018. Board presentation: 11/14/2018

  1. Let $f:A\to B$ and $g:B\to C$ be functions.
    1. If $g\circ f$ is injective, then $f$ is injective.
    2. If $g\circ f$ is surjective, then $g$ is surjective.
  2. Construct examples of functions $f:A\to B$ and $g:B\to C$ such that:
    1. $g\circ f$ is injective, but $g$ is not injective.
    2. $g\circ f$ is surjective, but $f$ is not surjective.
  3. Prove Prop. 9.15 (Hint: induction)
  4. Prove Prop. 9.18

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people/fer/330ws/fall2018/homework.txt · Last modified: 2018/11/16 14:44 by fer