Finite State Automata (FSA) with Output, Turing
Machines
Lecture Notes - week 12
1: FSA w/ output - Definition and Example 1
2: FSA w/ output - Example 2
3: FSA w/ output - Example 3
4: Definition - How does one FSA w/ output recognize (accept) a Language

Finite State Automata with NO output
( Lecture Notes - week 11 )
1: Finite State Automata (FSA) with NO output - Definition
2: FSA - An Example
3: FSA - The Example di-graph
4: Language - Definition, an Example
5: Regular Expression - definition
6: Regula

16
MATHEMATICS MAGAZINE
When Euler Met lHopital
WILLIAM DUNHAM
Muhlenberg College
Allentown, PA 18104
wdunham@muhlenberg.edu
We begin with a disclaimer: Leonhard Euler, born in Basel in 1707, never actually met
the multiply-named Guillaume Francois Antoin

Inha University in Tashkent
LINEAR ALGEBRA
Final Examination Preparation
COMPREHEMSIVE TEST
Fall Semester
J. Park
Nov. 29, 2015
POINTS
ATTENDENCE
5
HOMEWORK
15
MIDTERM
40
FINAL
60
TOTAL
120
Part I. Invertible matrix
.
find the inverse of by Gauss-Jo

The Helen of Geometry
John Martin
doi:10.4169/074683410X475083
John Martin (jmartin@santarosa.edu) received his BA in
math from Humboldt State College (1973) and his MA from
USC (1978). He teaches at Santa Rosa Junior College in
Santa Rosa CA where he has

174
MATHEMATICS MAGAZINE
Envelopes and String Art
GREGORY QUENELL
Plattsburgh State University
Plattsburgh, NY 12901
gregory.quenell@plattsburgh.edu
A familiar problem
For each [0, 1] let be the line segment in R2 connecting the point (, 0) with
the point

A Geometric Approach to Determinants
Author(s): John Hannah
Source: The American Mathematical Monthly, Vol. 103, No. 5 (May, 1996), pp. 401-409
Published by: Mathematical Association of America
Stable URL: http:/www.jstor.org/stable/2974931
Accessed: 16-0

SOLUTION
Linear Algebra
Fall, 2015
Show all your work neatly.
NO DETAILS, NO POINTS
1. Dimension Theory.
Let be a matrix such that
Find
(1) Find a basis of Row space of ,
(2) Find a basis of Nullspace of ,
and (3) Find .
Note that

Linear Algebra
Fall 2015
Inha University in Thashkent
Solution
Linear Algebra
J. Park
October 19, 2015
No point without solving process.
PART I. Algorithm
1. Find a general solution of the linear system
and list a set of vectors that span the soluti

Question 1 [F5151 with N0 output digraph]
Let M he the automaton with the following input set A, state set S with initial state 5'1): and accepting
(yes") state set Y:
1'1 = cfw_12, if, S = [5"], S], 32, Y = cfw_31
Suppose next state mclicn F ch is give