Homework Due March 1 - answers
Ch. 6, Problem 1: Find an isomorphism from the group of integers under
addition to the group of even integers under addition.
Solution: I will show that the map f (x) = 2x is an isomorphism. Any even integer is
of the form 2
INTRODUCTION:
VOCABULARY:
DISCUSSION:
Sec timing)”; and
Sol-Left:er
APCS - Java. Lesson 23
STUDENT OUTLINE
Lesson 23 — Quadratic Sorting Algorithms
In this lesson, you will learn about three sorting algorithms: bubble, selection,
and insertion. You are re
STUDENT OUTLiNE
Lesson 29 - Inheritance. Polymorphism. and Abstract Classes
DTRODCC'I'ION:
VDCABULARY:
DISCUSSIDN:
APCS — Java, Inseam 29
A class represents a set ct'objects that share the same structure and behaviors. The
class determines the structure o
STUDENT OUTLINE
Lesson 21 — Two-Dimensional Arrays
INTRODUCTION: Two—dimensional arrays allow the programmer to solve problems involving rows
and columns. Many data processing problems involve rows and columns. such
as an airplane reservation system or th
INTRODUCTION:
VOCABULARY:
DISCUSSION:
APCS Java. Lesson 20
STUDENT OUTLINE
Lesson 20 — ArrayList
It is very common for a program to manipulate data that is kept in a list. You
have already seen how this is done using arrays. Arrays are a ﬁmdamental featur
STUDENT OUTLINE
Lesson 16 — Text File no
INTRODUCTION: In this lesson you will learn about text ﬁle input and output using the classes
F; _ 0 Lip '_' ‘: and :"1. 1-: Cu; : Y: L; which are provided “Pith the library chntutif. The
source programs you have b
£5 3 LL\/ STUDENT OUTLINE
Lesson 19 — Single Dimension Arrays
INTRODUCTION: Programs often need a way to work with large amounts of data without declaring
thousands of scalar variables. in this lesson we explain the terms data structure
and algorithm, an
2.4 Essential Questions
Record your answers in your own words in your lab manual.
1. How do humans communicate with the world around them?
2. How does the power of sight allow humans to communicate with the
outside world?
3. What are the parts of the eye?
Jalen Heyward
Conclusion
1. Describe the path of an electrical impulse as it moves through a neuron. You
must use the words axon, axon terminal, dendrites, myelin sheath, nodes of
Ranvier, synapse and neurotransmitters in your description.
Electron impuls
2.2.5 Electrical Communication Brochure Assessment
Your task is to create a three-fold brochure that condenses your understanding of
this unit. Below you will find bullet pointed questions to guide you but the goal is to
show your understanding of how an
How our body goes through
communication:
The nervous system is made up of
neurons that communicate by sending
electrical messages down the axon
through action potential. The neuron then
picks up the message signal at the
dendrites, passes the signals down
There is a morn by men unseen
Emily Dickinson
There is a morn by men unseen
Whose maids upon remoter green
Keep their Seraphic May
And all day long, with dance and game
And gambol I may never name
Employ their holiday
Here to light measure, move the feet
The Grave
By Katherine Anne Porter
13-MINUTE READ ISSUE: Spring 1935
The grandfather, dead for more than thirty years, had been twice
disturbed in his long repose by the constancy and possessiveness of
his widow. She removed his bones first to Louisiana a
INTRODUCTION:
VOCAB ULARY:
DISCUSSION:
APCS - Java, Leison 27
STUDENT OUTLINE
Lesson 2? — Arrays of Objects
In previous lessons, the arrays sorted primitive types, such as integers and
characters. Arrays can also have references to objects as elements. Fa
STUDENT OUTLINE
Lesson 24 — Order of Algorithms
INTRODUCTION: The two criteria used for selecting a data structure and algorithm are the amount
of memory required and the speed of execution. The analysis of the speed of an
algorithm ids to a sumr'riar}r s
INTRODUCTION:
VOCABULARY:
DISCUSSION:
2:
STUDENT OUTLINE
Lesson 25 - Merge and Mergesort
In Lesson 23, we studied the quadratic sorting algorithms. We saw how the
number of steps required inereased as an N2 factor when sorting N elements In
the next two l
Assignment 3b
28, 29, 32, 49, 50, 67, 70, 72, 73
28. Suppose that H is a proper subgroup of Z under addition and that H contains 18, 30, and 40.
Determine H.
Since H is a subgroup it is closed under addition and subtraction (additive inverses) so we see
t
MATH 3005 Homework Solution
Han-Bom Moon
Homework 6 Solution
Chapter 6.
1. Find an isomorphism from the group of integers under addition to the group of
even integers under addition.
Let 2Z be the set of all even integers. Dene a map : Z 2Z as (n) = 2n.
W
HOMEWORK 3
1. (# 18) If H and K are subgroups of a group G, show that H K is a subgroup of G.
Proof. We need to show that H K is nonempty and that xy 1 H K for any x, y H K.
Since the identity element is in both H and K we have that H K = .
Let x, y H K.
STUDENT OUTLINE
Lesson 27 Arrays of Objects
INTRODUCTION:
In previous lessons, the arrays sorted primitive types, such as integers and
characters. Arrays can also have references to objects as elements. Fairly
common complex information management structu
STUDENT OUTLINE
Lesson 26 Quicksort
INTRODUCTION:
Quicksort is another recursive sorting algorithm that works by dividing lists in
half. Whereas mergesort divided lists in half and then sorts each sublist,
quicksort will roughly sort the entire list, and
STUDENT OUTLINE
Lesson 25 Merge and Mergesort
INTRODUCTION:
In Lesson 23, we studied the quadratic sorting algorithms. We saw how the
number of steps required increased as an N2 factor when sorting N elements. In
the next two lessons we will study two rec
STUDENT OUTLINE
Lesson 23 Quadratic Sorting Algorithms
INTRODUCTION:
In this lesson, you will learn about three sorting algorithms: bubble, selection,
and insertion. You are responsible for knowing how they work, but you do not
necessarily need to memoriz
STUDENT OUTLINE
Lesson 29 - Inheritance, Polymorphism, and Abstract Classes
INTRODUCTION:
A class represents a set of objects that share the same structure and behaviors. The
class determines the structure of objects by specifying variables that are conta
STUDENT OUTLINE
Lesson 24 Order of Algorithms
INTRODUCTION:
The two criteria used for selecting a data structure and algorithm are the amount
of memory required and the speed of execution. The analysis of the speed of an
algorithm leads to a summary state
STUDENT OUTLINE
Lesson 20 ArrayList
INTRODUCTION:
It is very common for a program to manipulate data that is kept in a list. You
have already seen how this is done using arrays. Arrays are a fundamental feature
of Java and of most programming languages. B
STUDENT OUTLINE
Lesson 16 Text File I/O
INTRODUCTION:
In this lesson you will learn about text file input and output using the classes
FileInput and FileOutput, which are provided with the library chn.util. The
source programs you have been writing are al
STUDENT OUTLINE
Lesson 19 Single Dimension Arrays
INTRODUCTION:
Programs often need a way to work with large amounts of data without declaring
thousands of scalar variables. In this lesson we explain the terms data structure
and algorithm, and then introd