IST 4 Information and Logic
|
|
|
- Silvia Daniel
- 5 years ago
- Views:
Transcription
1 IST 4 Information and Logic
2 Lectures are at: paradise.caltech.edu/ist4/lectures.html edu/ist4/lectures html
3 Homeworks are at: paradise.caltech.edu/ist4/homeworks.html edu/ist4/homeworks html
4 T = today x= hw#x out x= hw#x due mon tue wed thr fri 31 M1 1 7 M1 T oh oh 14 oh 1 oh 2M2 21 oh oh 2 Mx= MQx out 28 oh M2 oh oh = office hours oh 3 4 oh oh midterms oh Mx= MQx due 19 oh oh oh 5 oh oh oh
5 MQ1 Everyone has a gift! Due Thursday 4/10/2012 by 10pm Please PDF lastname-firstname.pdf to ta4@paradise.caltech.edu
6 Languages help in reasoning beyond our natural sense What is our number sense? Need a language g for quantities!
7 What is this item? Lebombo bone ~40, years ago hint? A very early device for recording quantities by making marks on a bone of a monkey
8 Early Counting Devices ~40,000 ago lebombo bone 1970's excavations in Lebombo Mountains, a piece of the fibula of a baboon was found marked with 29 clearly defined notches???
9
10 Lunar cycle (month): ~29.5 days Source: Wikipedia
11 Day and night: 2 10 Moon Earth (month): ~29 days Earth Sun (year): ~365 days
12
13 Igno-Info break 12 is a special number.. Examples?
14 ~150, years ago: modern humans - Homo sapiens ~50,000 years ago: emergence of languages ~5,000 years ago: emergence of written languages ~500 years ago: emergence of printing ~50 years ago: emergence of electronic forms
15 What was invented nt first? a. Written text 1. Numbers a and 1 together BC: writing was used for accounting... Denise Schmandt-Besserat Source: Her 2009 paper, Tokens and Writing: the Cognitive Development, Will be posted on the class web page
16 Tokens 8,000 ya Physical Symbols: shape = meaning Source: DSB 2009 paper
17 Idea: Represent goods with tokens one garment one jar of oil one ingot of metal one sheep Token are physical symbols of real items a language! one honeycomb one garment Source: DSB 2009 paper
18 Secure Transactions: Envelopes (Bulla) and Seals, 3,700BC
19 cylinder Seals
20 New Idea: Mark on the outside what is inside... Writing: physical symbols to imprintedi symbols Envelope showing the imprint of three ovoid tokens with an incised line representing jars of oil Source: DSB 2009 paper 3,300 BC
21 A crazy idea: No need for an envelope! The tablet is born! Tablet showing the impression of spheres and cones representing measures of grain 3,100BC Source: DSB 2009 paper
22 One more crazy idea: Separate between the quantity and the item... Too many jars of oils for markings on the envelope / tablet Source: DSB 2009 paper
23 Separate between the quantity and the item... The NUMBER is born!!! Twelve jars Language for quantities!!! Source: DSB 2009 paper
24 ten one tablet featuring an account of 33 measures of oil, 3,100 BC oil Source: DSB 2009 paper
25 Language for quantities!!! The item (jar of oil) is not restricted to accounting... Not restricted to envelopes General writing is born!!! A great story... Not covered in IST4
26 Where did it start?
27 Babylonians and Egyptians ~5000 years ago
28 The Egyptians Preferred 10 How will you represent a trillion 1,000,000,000,000? 2x x10 + 6x1 = 276
29 Babylonians The first Positional number system 1 10 The Babylonian preferred 60
30 Babylonians The first Positional number systems 4x x1 = 276
31 Babylonians were Masters of Abstractions Why 60? Good for computation and representing fractions: 1/2 = 30/60 1/3 = 20/60 1/4 = 15/60 1/5 = 12/60 1/6 = 10/60
32 Babylonian Number Systems What is the number? 31 What is the number? 31x = 1891
33
34 The Babylonians knew everything!
35 How did we learn about the Babylonians? Expeditions (Ninveh, Nippur...): -Claudius Rich Paul-Émile Botta Austen Layard Peters and Hilprecht, U Penn (4) -Chicago, U. Penn, (19) Hilprecht (Ed), Babylonian Expeditions, U. of Pennsylvania, 1906
36 Born in Poland PhD in Italy Professor in Chicago Deciphering the code Ignace Jay Gelb
37 A tablet called: Plimpton 322, from 1800 BC, at Columbia U 9x13 cm
38 Austria (BS) > Germany (BS) > Denmark (PHD) > US (Brown U) Otto Neugebauer Mathematics > History of Exact Sciences His son: Gerry Neugebauer (PhD 60) Millikan Professor of Physics, Emeritus
39 Mathematics > Teaching Math ->History of Exact Sciences Asger Aaboe Denmark > US (PhD 1957, Brown U) -> 1961,Yale U Otto Neugebauer
40 Asger Aaboe Otto Neugebauer Today, you will get to be Otto and Asger!
41 Multiplication table for ? , , , ,30?? 1,39 1, ,57 2,6 2,15 2,24 2,33 2, ,51 3,0 4,30 6,0 7,30
42 Multiplication instead of division??
43
44
45 fraction
46 7 and 11 and other numbers are missing? fraction
47 Regular numbers = divide 60 n A number that its prime factors are at most 5: 5-smooth Is 24 a regular number? 2x2x2x3 Is 896 a regular number? 2x2x2x2x2x2x2x7 Is 900 a regular number? 2x2x3x3x5x5 Generate all the regular numbers??
48 Regular numbers = divide 60 n Also: 5-smooth, Hamming numbers 1 81 Appear in the Babylonian tablet Source: Wikipedia
49 -The Babylonians had multiplication and reciprocals tables for the regular numbers + the number 7 -Also they had tables of squares -And many tricks... We call it algorithms... Question: Suppose you can add, subtract, have small multiplication tables, large tables for n 2, can you use it to compute arbitrary multiplications?
50 The Babylonians knew everything! even Geometry
51 The Babylonians knew everything! even Geometry
52 The Babylonians knew everything! even Geometry
53 The Babylonians knew everything! even Geometry again!! 12?12 2,24
54 Which Number Does not Belong? is a space between two digits
55 Which Number Does not Belong?
56 Positional number systems
57 Base-10 is embedded in our language and thought Base-b Positional Systems
58 Translation between languages! Base-b Conversion n to Base-B B
59 Translation between languages! Base-b Conversion n to Base-B B b Base b to base Base 10 to base B B Sum the corresponding weights using base-10 arithmetic Successive division by B using base-10 arithmetic
IST 4 Information and Logic
IST 4 Information and Logic Lectures are at: paradise.caltech.edu/ist4/lectures.html edu/ist4/lectures html Homeworks are at: paradise.caltech.edu/ist4/homeworks.html edu/ist4/homeworks html T = today
IST 4 Information and Logic
IST 4 Information and Logic MQ1 Everyone has a gift! Due Today by 10pm Please email PDF lastname-firstname.pdf to ta4@paradise.caltech.edu HW #1 Due Tuesday, 4/12 2:30pm in class T = today x= hw#x out
IST 4 Information and Logic
IST 4 Information and Logic MQ1 Computers outperform the human brain? Due Today by 10pm Have your name inside the file as well... Please email PDF lastname-firstname.pdf to istta4@paradise.caltech.edu
IST 4 Information and Logic
IST 4 Information and Logic MQ1 Everyone has a gift! Due Today by 10pm Please email PDF lastname-firstname.pdf to ta4@paradise.caltech.edu HW #1 Due Tuesday, 4/14 230 2:30pm in class T = today x= hw#x
IST 4 Information and Logic
IST 4 Information and Logic Quizzes grade (6): average of top n-2 T = today x= hw#x out x= hw#x due mon tue wed thr fri 1 M1 oh 1 8 oh M1 15 oh 1 T 2 oh M2 22 oh PCP oh 2 oh sun oh 29 oh M2 oh = office
IST 4 Information and Logic
IST 4 Information and Logic mon tue wed thr fri sun T = today 3 M oh x= hw#x out oh M 7 oh oh 2 M2 oh oh x= hw#x due 24 oh oh 2 oh = office hours oh oh T M2 8 3 oh midterms oh oh Mx= MQx out 5 oh 3 4 oh
IST 4 Information and Logic
IST 4 Information and Logic HW2 will be returned today Average is 53/6~=88% T = today x= hw#x out x= hw#x due mon tue wed thr fri 3 M 6 oh M oh 3 oh oh 2M2M 2 oh oh 2 Mx= MQx out 27 oh M2 oh oh = office
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 3 M 7 oh M 4 oh oh 2M2 2 oh oh 2 oh T Mx= MQx out 28 oh M2 oh oh = office hours 5 3 2 oh 3 4 oh oh midterms oh Mx= MQx
IST 4 Information and Logic
IST 4 Information and Logic mon tue wed thr fri sun T = today 3 M oh x= hw#x out 0 oh M 7 oh oh 2 M2 oh oh x= hw#x due 24 oh oh 2 oh = office hours oh oh M2 8 3 oh midterms oh oh Mx= MQx out 5 oh 3 4 oh
IST 4 Information and Logic
IST 4 Information and Logic mon tue wed thr fri sun T = today 3 M oh x= hw#x out oh M 7 oh oh 2 M2 oh oh x= hw#x due 24 oh oh 2 oh = office hours oh oh M2 8 3 oh midterms oh oh Mx= MQx out 5 oh 3 4 oh
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M 6 oh M oh 3 oh oh 2M2M 20 oh oh 2 27 oh M2 oh midterms Students MQ oh = office hours Mx= MQx out 4 3 oh 3 4 oh oh
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 31 M1 1 7 oh M1 14 oh 1 oh 2M2 21 oh oh 2 oh Mx= MQx out 28 oh M2 oh oh = office hours 5 3 12 oh 3 4 oh oh T midterms oh
IST 4 Information and Logic
IST 4 Information and Logic T = today mon tue wed thr 3 M1 oh 1 fri sun x= hw#x out 10 oh M1 17 oh oh 1 2 M2 oh oh x= hw#x due 24 oh oh 2 Mx= MQx out 1 oh M2 oh = office hours oh T 8 3 15 oh 3 4 oh oh
IST 4 Information and Logic
IST 4 Information and Logi T = today x= hw#x out x= hw#x due mon tue wed thr fri 3 M 7 oh M 4 oh oh 2M2 2 oh oh 2 oh 28 oh M2 oh oh = offie hours 5 3 Mx= MQx out 2 oh 3 4 oh oh midterms oh Mx= MQx due
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M1 1 6 oh M1 oh 13 oh 1 oh 2M2M 20 oh oh 2 Mx= MQx out 27 oh M2 h T oh = office hours oh T 4 3 11 oh 3 4 oh oh midterms
1-1. welcome to Chem 1A. this is Lec C I am Professor Penner
1-1 welcome to Chem 1A this is Lec C - 40030 I am Professor Penner 1-2 in this lecture about Chem 1A about Chemistry atoms - the building block. who knew? (and how did we find out) you are a select group
The Origins of Mathematics. Mesopotamia
The Origins of Mathematics in Mesopotamia The ancient Egyptians made their number system more efficient by introducing more symbols. The inhabitants of Mesopotamia (our book calls them Babylonians) achieved
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M1 1 6 oh M1 oh 13 oh 1 oh 2M2M 20 oh oh 2 T Mx= MQx out 27 oh M2 oh oh = office hours 4 3 11 oh 3 4 oh oh midterms
DIRECTIONS: Complete each of the enclosed activities and then use what you learn along with prior knowledge to fill in the outline below:
DIRECTIONS: Complete each of the enclosed activities and then use what you learn along with prior knowledge to fill in the outline below: I. Geography of Sumer A. Located in modern-day B. Between two rivers
Senior Math. Binary numbers are based on the powers of 2: 2 0 = 1, 2 1 = 2, 2 2 = 4, 2 3 = 8, 2 4 = 16, Binary numbers use only two digits: 0 and 1
Academic Coaches Conference Senior Math Senior Math Fertile Crescent I. Numeration Systems 12% A. Binary (base 2) and Sexagesimal (base 60) Systems B. Convert to and from base 10 C. Add and subtract in
INTRODUCTION TO INTEGERS
1 INTRODUCTION TO INTEGERS A. WHAT IS AN INTEGER? Integers are numbers made from natural numbers. On a number line, the arrows on either side of it would extend in opposite directions to include integers.
Relationships Between Quantities
Algebra 1 Relationships Between Quantities Relationships Between Quantities Everyone loves math until there are letters (known as variables) in problems!! Do students complain about reading when they come
Astronomy 122 Section 1 TR Digital Computer Laboratory. Outline. Class Webpage. Book Website
Astronomy 122 Section 1 TR 1300-1350 1320 Digital Computer Laboratory Leslie Looney Phone: 244-3615 Email: lwlw@wuiucw. wedu Office: Astro Building #218 Office Hours: Next Class: T 10:30-11:30 a.m. or
Clock Arithmetic. 1. If it is 9 o clock and you get out of school in 4 hours, when do you get out of school?
Clock Arithmetic We are going to learn all about clock addition and the relationship to remainders when you divide numbers. 1 Standard Clock Addition 1. If it is 9 o clock and you get out of school in
PHYSICS 100. Introduction to Physics. Bridges the gap between school science and Physics 101, Physics 120, Physics 125 or Physics 140
PHYSICS 100 Introduction to Physics Bridges the gap between school science and Physics 101, Physics 120, Physics 125 or Physics 140 Only for those WITHOUT Physics 12 or equiv. (C+ or better). If you have
AS 101: The Solar System (Spring 2017) Course Syllabus
AS 101: The Solar System (Spring 2017) Course Syllabus Instructor: Professor Wen Li Office: CAS 501 Phone: 617-353-7439 Email: wenli77@bu.edu Office hours: Mondays 3:30 5:00 pm, Wednesdays 3:30 5:00 pm,
Grade 7/8 Math Circles Winter March 20/21/22 Types of Numbers
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Winter 2018 - March 20/21/22 Types of Numbers Introduction Today, we take our number
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out mon tue wed thr fri 31 M1 1 7 oh M1 14 oh 1 oh 2M2 oh x= hw#x due 21 oh oh 2 T Mx= MQx out 28 oh M2 oh oh = office hours 5 3 12 oh 3 4 oh oh midterms oh
California 5 th Grade Standards / Excel Math Correlation by Lesson Number
(Activity) L1 L2 L3 Excel Math Objective Recognizing numbers less than a million given in words or place value; recognizing addition and subtraction fact families; subtracting 2 threedigit numbers with
AMA1D01C Egypt and Mesopotamia
Hong Kong Polytechnic University 2017 Outline Cultures we will cover: Ancient Egypt Ancient Mesopotamia (Babylon) Ancient Greece Ancient India Medieval Islamic World Europe since Renaissance References
California 3 rd Grade Standards / Excel Math Correlation by Lesson Number
California 3 rd Grade Standards / Lesson (Activity) L1 L2 L3 L4 L5 L6 L7 L8 Excel Math Lesson Objective Learning about the tens place and the ones place; adding and subtracting two-digit numbers; learning
MATH 205 L01 W 2006 MIDTERM AND SOLUTIONS
MATH 205 L01 W 2006 MIDTERM AND SOLUTIONS 1. For each of the following answer True or. Do not write T or F. [20] (a) Fermat is famous for his proof of the infinitude of primes. (b) The 10 Euro bill has
The Most Important Thing for Your Child to Learn about Arithmetic. Roger Howe, Yale University
The Most Important Thing for Your Child to Learn about Arithmetic Roger Howe, Yale University Abstract The paper argues for a specific ingredient in learning arithmetic with understanding : thinking in
Reclaiming Meaning in Mathematics
Reclaiming Meaning in Mathematics A Presentation for the WSCC 2007 Mathematics Conference William Bricken, PhD Lake Washington Technical College william.bricken@lwtc.edu For Teachers An educational chasm
Egyptian Mathematics
Egyptian Mathematics Dr. Carmen Bruni David R. Cheriton School of Computer Science University of Waterloo November 1st, 2017 Three Part Series Egyptian Mathematics Diophantus and Alexandria Tartaglia,
CHAPTER (multiply by 10) 2 10 (double first line) 4 20 (double third line) 8 40 (double fourth line) (halve first line)
CHAPTER 1 1. The answers are given in the answer section of the text. For the Egyptian hieroglyphics, 375 is three hundreds, seven tens and five ones, while 4856 is four thousands, eight hundreds, five
St. Ann s Academy - Mathematics
St. Ann s Academy - Mathematics Students at St. Ann s Academy will be able to reason abstractly and quantitatively. Students will define, explain, and understand different types of word problems (simple
AST 2002 Introduction to Astronomy
AST 2002 Introduction to Astronomy Recommended Textbooks The Cosmic Perspective The Essential Cosmic Perspective The Cosmic Perspective Fundamentals 8th Edition (Publisher: Pearson) Authors: Bennett, Donohue,
AS 102 The Astronomical Universe (Spring 2010) Lectures: TR 11:00 am 12:30 pm, CAS Room 316 Course web page:
Instructor: AS 102 The Astronomical Universe (Spring 2010) Lectures: TR 11:00 am 12:30 pm, CAS Room 316 Course web page: http://firedrake.bu.edu/as102/as102.html Professor Tereasa Brainerd office: CAS
Mr. Miles 8 th Grade Math Class Info & Syllabus
Mr. Miles 8 th Grade Math Class Info & Syllabus Welcome to 8 th grade! I look forward to getting to know you and help you learn some more awesome math this year! Please read the Class Info and attached
AS102 -The Astronomical Universe. The boring details. AS102 - Major Topics. Day Labs - Rooms B4 & 606. Where are we (earth, sun) in the universe?
AS102 - Major Topics Where are we (earth, sun) in the universe? What are stars? AS102 -The Astronomical Universe Instructor: Professor Tereasa Brainerd TAs: Ren Cashman & Katie Garcia How are stars born,
Grade 6 Math Circles. Ancient Mathematics
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Introduction Grade 6 Math Circles October 17/18, 2017 Ancient Mathematics Centre for Education in Mathematics and Computing Have you ever wondered where
FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY
5-453 FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY 5-453 FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY YOU NEED TO PICK UP THE SYLLABUS, THE COURSE SCHEDULE, THE PROJECT INFO SHEET, TODAY S CLASS NOTES
Course Staff. Textbook
Course Staff CS311H: Discrete Mathematics Intro and Propositional Logic Instructor: Işıl Dillig Instructor: Prof. Işıl Dillig TAs: Jacob Van Geffen, Varun Adiga, Akshay Gupta Class meets every Monday,
Mesopotamia Here We Come
Babylonians Mesopotamia Here We Come Chapter The Babylonians lived in Mesopotamia, a fertile plain between the Tigris and Euphrates rivers. Babylonian society replaced both the Sumerian and Akkadian civilizations.
Monday May 12, :00 to 1:30 AM
ASTRONOMY 108: Descriptive Astronomy Spring 2008 Instructor: Hugh Gallagher Office: Physical Science Building 130 Phone, Email: 436-3177, gallagha@oneonta.edu Office Hours: M 2:00-3:00 PM, Th 10:00-11:00
APTITUDE & MENTAL ABILITY SOLUTIONS
TNPSC DEO PRELIMINARY EXAM [0.03.019] APTITUDE & MENTAL ABILITY SOLUTIONS 1. If the average of the values 9, 6, 7, 8, 5 and x is 8. Find the value of x. A. 1 B. 13 C. 10 D. 9. Find the standard deviation
Math 211 Lecture Notes: Sections
Math 211 Lecture Notes: Sections 1.1-1.3 Richard Blecksmith 1. Math 211 Business Calculus Section 1 Summer, 2009 Mon, Tues, Wed, Thurs 8:00-9:15 a.m. Reavis Hall 201 Independence Day Holiday is Wednesday,
ISP 205: Visions of the Universe. Your Professor. Assignments. Course Resources
ISP 205: Visions of the Universe Goal To learn about the universe around us Astronomy Have fun Method Lectures Collaborative learning Hands-on activities Assessment Homework Electronic postings Quizzes
Fall 2017 September 20, Written Homework 02
CS1800 Discrete Structures Profs. Aslam, Gold, & Pavlu Fall 2017 September 20, 2017 Assigned: Wed 20 Sep 2017 Due: Fri 06 Oct 2017 Instructions: Written Homework 02 The assignment has to be uploaded to
Written in Stone UNIT 2 WEEK 1. Read the article Written in Stone before answering Numbers 1 through 5. Weekly Assessment Unit 2, Week 1 Grade 6 61
Read the article Written in Stone before answering Numbers 1 through 5. UNIT 2 WEEK 1 Written in Stone People need to communicate. The earliest human beings most likely communicated with sounds and gestures.
(Check Off Completed/ Corrected Items) Pg. 2-3: MSA 3.2 Exploring Equality. Pg. 5-7: MSA 3.3 Writing Equations. Layered Book Exit Ticket 2
Moving Straight Ahead: Linear Relationships Name: Per: Investigation 3: Solving Equations 7.EE.B.4: Use variables to represent quantities in the real world or mathematical problem, and construct simple
Astro 210 Lecture 3 Jan 22, 2018
Astro 210 Lecture 3 Jan 22, 2018 Announcements HW1 available; due online in pdf at 5:00pm Friday Office hours: Instructor 2-3pm Wed; TA 3:30-4:30pm Thurs register your iclicker; link on course moodle site
Math 90 Lecture Notes Chapter 1
Math 90 Lecture Notes Chapter 1 Section 1.1: Introduction to Algebra This textbook stresses Problem Solving! Solving problems is one of the main goals of mathematics. Think of mathematics as a language,
18.2 Earth Cycles Days and years Calendars Years and days Leap years Calendars throughout human history 20,000 years ago. 7,000 BC. 4,000 BC.
18.2 Reading 18.2 Earth Cycles Do you ever wonder where our calendar comes from? Or why the Moon gradually changes its shape? Or why we have seasons? The answers have to do with the relative positions
Handouts. CS701 Theory of Computation
Handouts CS701 Theory of Computation by Kashif Nadeem VU Student MS Computer Science LECTURE 01 Overview In this lecturer the topics will be discussed including The Story of Computation, Theory of Computation,
History of the Pythagorean Theorem
History of the Pythagorean Theorem Laura Swenson, (LSwenson) Joy Sheng, (JSheng) Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of
Math 10C Course Outline
Math 10C Course Outline Mr. Collin Dillon St. Joseph Catholic High School 8:40am-9:55am Phone (780) 532-7779 Email CollinDillon@gpcsd.ca Mr. Dillon s Website The essence of mathematics is not to make simple
Numbers and Counting. Number. Numbers and Agriculture. The fundamental abstraction.
Numbers and Counting Number The fundamental abstraction. There is archaeological evidence of counters and counting systems in some of the earliest of human cultures. In early civilizations, counting and
Text 3: Discoveries in Africa and Beyond. Topic 1: The Origins of Civilization (Prehistory B.C.E) Lesson 1: Learning About Our Past
Text 3: Discoveries in Africa and Beyond Topic 1: The Origins of Civilization (Prehistory - 300 B.C.E) Lesson 1: Learning About Our Past Discoveries in Africa and Beyond Since the 1870s, scholars have
From Hipparchus to a Helix Ruler
From Hipparchus to a Helix Ruler Jerold Mathews This paper gives a brief history of the chord function { a precursor of the sine function { from the mathematics/astronomy of Hipparchus and Ptolemy to the
Announcements Monday, September 18
Announcements Monday, September 18 WeBWorK 1.4, 1.5 are due on Wednesday at 11:59pm. The first midterm is on this Friday, September 22. Midterms happen during recitation. The exam covers through 1.5. About
Math 58 Test # 3 Fall 2014 Chapter 9, Part 1 Instructor: Smith-Subbarao
Math 58 Test # 3 Fall 2014 Chapter 9, Part 1 Instructor: Smith-Subbarao Solutions Name Score: If you are not sure about notation, please ask for help! (4 + 1 ) / x means 4 + 1 is in numerator and x is
Calculus Differential Integral
Calculus Differential Integral 1 / 6 2 / 6 3 / 6 Calculus Differential Integral Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus) is the mathematical
Physics 101 covers. Forces Kinematics Energy/Momentum Rotations Fluids Waves/Sound Thermodynamics. Physics 101: Lecture 1, Pg 1
Physics 101 covers Forces Kinematics Energy/Momentum Rotations Fluids Waves/Sound Thermodynamics Physics 101: Lecture 1, Pg 1 Meet the Lecturer Professor Tom Kuhlman tkuhlman@illinois.edu Office Hours
Math 31 Lesson Plan. Day 5: Intro to Groups. Elizabeth Gillaspy. September 28, 2011
Math 31 Lesson Plan Day 5: Intro to Groups Elizabeth Gillaspy September 28, 2011 Supplies needed: Sign in sheet Goals for students: Students will: Improve the clarity of their proof-writing. Gain confidence
PS 101: Introductory Astronomy Fall 2014
PS 101: Introductory Astronomy Fall 2014 Lecture: Lab: Tues./Thurs. 12:00 pm - 1:15 pm, S166 Tues. 4:00 pm - 5:50 pm, S166 Instructor: Dr. Jon M. Saken Office: S178 (Science Bldg.) Phone: 696-2753 E-mail:
Welcome to Math 102 Section 102
Welcome to Math 102 Section 102 Mingfeng Qiu Sep. 5, 2018 Math 102: Announcements Instructor: Mingfeng Qiu Email: mqiu@math.ubc.ca Course webpage: https://canvas.ubc.ca Check the calendar!!! Sectional
CS483 Design and Analysis of Algorithms
CS483 Design and Analysis of Algorithms Lecture 1 Introduction and Prologue Instructor: Fei Li lifei@cs.gmu.edu with subject: CS483 Office hours: Room 5326, Engineering Building, Thursday 4:30pm - 6:30pm
Unit 1 Writing and Evaluating Algebraic Expressions
CC Math 1A Name Unit 1 Writing and Evaluating Algebraic Expressions Day Date Lesson Assignment Mon 8/25 Lesson 1 Writing and Evaluating Algebraic Expressions Tues 8/26 Lesson 2 Combining Like Terms & Distributive
Section 4.2. Place-Value or Positional- Value Numeration Systems. Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 4.2 Place-Value or Positional- Value Numeration Systems What You Will Learn Place-Value or Position-Value Numeration Systems 4.2-2 Place-Value System (or Positional-Value System) The value of the
PHYS 1020 General Physics. This image is from the wikimedia commons. File:Luna_Park_Melbourne_scenic_railway.
PHYS 1020 General Physics This image is from the wikimedia commons. http://commons.wikimedia.org/wiki/ File:Luna_Park_Melbourne_scenic_railway.jpg (Erich)Werner Ens 518 Allen Office Hours: MW 9:30-10:30
Chemistry 14C: Structure of Organic Molecules - Winter 2017 Version 56
Chemistry 14C: Structure of Organic Molecules - Winter 2017 Version 56 Instructor: Dr. Steven A. Hardinger Office: Young Hall 3077C harding@chem.ucla.edu Office hours: Monday and Tuesday 2:00-2:50 PM Teaching
CS Module 1. Ben Harsha Apr 12, 2017
CS 50010 Module 1 Ben Harsha Apr 12, 2017 Course details Course is split into 2 modules Module 1 (this one): Covers basic data structures and algorithms, along with math review. Module 2: Probability,
CSE 311: Foundations of Computing I. Lecture 1: Propositional Logic
CSE 311: Foundations of Computing I Lecture 1: Propositional Logic Some Perspective Computer Science and Engineering Programming CSE 14x Theory Hardware CSE 311 About the Course We will study the theory
Linear Functions, Equations, and Inequalities
CHAPTER Linear Functions, Equations, and Inequalities Inventory is the list of items that businesses stock in stores and warehouses to supply customers. Businesses in the United States keep about.5 trillion
Section 1.2 Factors and Factor Operators
Section 1. Factors and Factor Operators The most basic component of mathematics is the factor. Factors are parts of multiplication, therefore, in the product or or the factors are and. And, since 1, we
Making Math: A Hands on History Beth Powell
Making Math: A Hands on History Beth Powell My City School, San Francisco, CA bethciis@yahoo.com Why Study the History of Math Full of Epic Failures Creates a Sense of Wonder Connections, Integration,
Hie-Joon Kim. Professor Emeritus Seoul National University. Experience. Representative Publications
Hie-Joon Kim Professor Emeritus Seoul National University B.S. Chemistry, Seoul National University, Korea, 1970 Ph.D. Chemistry, University of Chicago, USA, 1977 Experience Professor, Department of Chemistry
AS The Astronomical Universe. Prof. Merav Opher - Fall 2013
SYLLABUS AS 102 - The Astronomical Universe Prof. Merav Opher - Fall 2013 Course Catalog Summary: The birth and death of stars; red giants, white dwarfs, black holes; our galaxy, the Milky Way, and other
SAMPLE EVALUATION ONLY
TOPIC 2 Integers 2.1 Overview Why learn this? Integers are whole numbers that can be positive or negative. There are many examples in everyday life where an understanding of integers is useful, such as
CS 340: Discrete Structures for Engineers
CS 340: Discrete Structures for Engineers Instructor: Prof. Harry Porter Office: FAB 115-06 harry@cs.pdx.edu Hours: Mon 3-4, Wed 3-4, or by appointment Website: web.cecs.pdx.edu/~harry/discrete Class Mailing
Contents. To the Teacher... v
Katherine & Scott Robillard Contents To the Teacher........................................... v Linear Equations................................................ 1 Linear Inequalities..............................................
Is this in correct scientific notation form? If not, explain. If correct, explain how you know x 10 4
December 1, 2014 Unit 2c - Scientific Notation Standards: MCC8.EE.3, MCCG8.EE.4 MCC8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. MCC8.EE.2: Evaluate
Now on to scales in the. Let s change scale by TWO orders of magnitude at a time and see what happens.
Announcements Read 2.1 (Magnitude & Flux), 3.1, 3.2, 3.3 In-class Quiz #1 on Tuesday, January 29. Homework #2 due in class on Thursday, January 31. Disability Services is in need of a note taker for this
Number Theory. Jason Filippou UMCP. ason Filippou UMCP)Number Theory History & Definitions / 1
Number Theory Jason Filippou CMSC250 @ UMCP 06-08-2016 ason Filippou (CMSC250 @ UMCP)Number Theory History & Definitions 06-08-2016 1 / 1 Outline ason Filippou (CMSC250 @ UMCP)Number Theory History & Definitions
Using Algebra Fact Families to Solve Equations
Using Algebra Fact Families to Solve Equations Martin V. Bonsangue, California State University, Fullerton Gerald E. Gannon, California State University, Fullerton
Introduction to Integers
Introduction to Integers Get the Point? Lesson 7-1 Integers and the Number Line Lesson Targets: Use integers to represent quantities in real-world contexts. Position and identify integers on a number line.
Week 2: Reading, Practice Problems, and Homework Exercises
Calculus III E Term, Sections E0 and E96 Instructor: E.M. Kiley Due Friday, July, 05, :59 p.m. Wee : Reading, Practice Problems, and Homewor Exercises Reminder Your submitted homewor solutions should show
Goals of the day. Who should take this course? MATH REVIEW SESSION: ASTR 1120 General Astronomy: Stars & Galaxies
ASTR 1120 General Astronomy: Stars & Galaxies Prof. Rosalba Perna TA:Thomas Rogers http://amalfi.colorado.edu/~rosalba/astro1120/astro1120.html MAKE SURE TO GO OVER THE SYLLABUS (if you haven t already
ASTRONOMY 10 De Anza College
ASTRONOMY De Anza College Section 1 M - F, 7:0-8: am De Anza Planetarium (PLT) ek Cichanski Office: S-1a Office hours: Mon thru Fri :0am-:pm, other times by appt. Office phone: (408) 84-84 Email: cichanskimarek@fhda.edu
Section 5.1 Supplement Number Problems
Number Problems Why do we need to learn math and how is the math that we learn useful to us? Chapter 5 will begin to answer these concerns. To resolve any real world problem with math, one must first be
Admin. ! Will post sample questions soon. 1. Choose a bit-length k. 2. Choose two primes p and q which can be represented with at most k bits
Admin Assignment 6 Midterm reviews Tue & Wed! Will post sample questions soon ENCRYPTION TAKE 2: PRACTICAL DETAILS Assignment 7 Office hours end today at 3:40 (instead of 4) David Kauchak CS52 Spring 2016
Venus - Overview. Exploration of Venus. Admin. 9/26/17. Second planet from Sun Earth s sister planet
Admin. 9/26/17 1. Class website http://www.astro.ufl.edu/~jt/teaching/ast1002/ 2. Optional Discussion sections: Tue. ~11.30am (period 5), Bryant 3; Thur. ~12.35pm (end of period 5 and period 6), start
All numbered readings are from Beck and Geoghegan s The art of proof.
MATH 301. Assigned readings and homework All numbered readings are from Beck and Geoghegan s The art of proof. Reading Jan 30, Feb 1: Chapters 1.1 1.2 Feb 6, 8: Chapters 1.3 2.1 Feb 13, 15: Chapters 2.2
Homework #4. sun Bemine
IDS 102 Homework #4 Name 1. Why is it warmer (on the average) in Auburn in July than it is in Auburn in January? Explain your reasoning. (Draw a diagram if that will help!) 2. A new planet has just been
Getting Ready for Grade 4 Test Lessons 1 11
Lessons 1 11 Use the space on the page to do your work. Then mark the answer you have chosen. If you change your answer, be sure to erase completely. 1 Annie s sister goes to a college that has 16,374
CHEMISTRY 121 FG Spring 2013 Course Syllabus Rahel Bokretsion Office 3624, Office hour Tuesday 11:00 AM-12:00 PM
CHEMISTRY 121 FG Spring 2013 Course Syllabus Rahel Bokretsion rbokretsion@ccc.edu Office 3624, Office hour Tuesday 11:00 AM-12:00 PM GENERAL COURSE INFORMATION Required Material: Introductory Chemistry
Math 202 notes. Jason Riedy. 27 August, Review 1. 2 Ruling out possibilities Logic puzzles The pigeonhole principle 2
Math 202 notes Jason Riedy 27 August, 2008 Contents 1 Review 1 2 Ruling out possibilities 1 2.1 Logic puzzles............................. 2 3 The pigeonhole principle 2 4 Mathematical reasoning 3 5 Next
AY2 Introduction to Astronomy Winter quarter, 2013
AY2 Introduction to Astronomy Winter quarter, 2013 Instructor: Maria Fernanda (Feña) Duran (mfduran@ucolick.org) Teaching assistants: Jieun Choi (jchoi37@ucsc.edu) Katie Hamren (khamren@ucolick.org) Course