## lazy idle little schemer

Posted by vlorbik on September 24, 2010

i’m back at work slinging the math.

i’ve posted a few details in MEZB.

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## Anonymous said

Mathematics 366: Discrete Mathematical Structures 1

Autumn Quarter 2010

Owen Thomas MW 152

Phone: 292-0244 (Office)

704-4531 (Cel)

Office Hours: TR 4:00-5:20

(and by appointment)

Catalog Number: 12901

Course ID: 115508

TR 5:30–6:48 PM

University Hall 051

Text: Discrete Mathematics with Applications, Susanna S. Epp

(4th Edition; Brooks/Cole 2011 ISBN 0495391328)

Sections Covered: 2.1–2.4… 3.1–3.4… 4.1–4.6… 5.1–5.4… 6.1–6.3… 8.1… 7.1–7.3

Catalogue Description:

Mathematical formalization and reasoning, logic and Boolean algebra; sets, functions, relations, recursive definitions, and mathematical induction; and elementary counting techniques.

Prerequisite: Mathematics 132 or 152.xx

Follow-up Course: Math 566

## vlorbik said

http://www.ureg.ohio-state.edu/ourweb/more/Content/bigcal_pdf.pdf

quarter calendar

http://www.math.ohio-state.edu/~carlson/09sp366.html

carlson’s spring 09 notes

## vlorbik said

\hskip1.7in Name: \null\nobreak\leaders\hrule\hskip10pt plus1filll\ \par%

\smallskip

\centerline{Math 366}

\centerline{Exam 2: November 4, 2010.}

\vskip .5in

\parindent=0

{\bf 1.}

Compute the sum: $\sum_{i=1}^3 i^3$.

\vfil

{\bf 2.}

Prove by induction: $(\forall n \in {\Bbb Z}^+) 6|(7^n -1)$.

(“For every integer $n$ greater than or equal to 1,

six divides $7^n -1$”.)

\vfil\vfil\vfil\vfil

\vfil\eject

{\bf 3.}

Prove that whenever $a$ {\bf mod }$6=3$

and $b$ {\bf mod} $6=2$, it is also true

that $ab$ {\bf mod} $6=0$.

(Remark: this shows that the “Zero

Product Law” $(a \not= 0 \wedge b\not=0)

\rightarrow (ab\not=0)$ is false in

certain number systems.)

\vfil

{\bf 4.}

Prove that

$(\forall x, y \in {\Bbb Q}) xy \in {\Bbb Q}\, .$

(“The product of any two rational numbers is

a rational number”.)

\vfil\eject

{\bf 5.}

Prove by contradiction that

there is no greatest Real

number less than 17.

\vfil

{\bf 6.}

Prove that there is an odd integer $k$

such that $k$ {\bf mod} $7 = 4$.

\vfil\eject

\bye