SlideShare a Scribd company logo
1 of 24
Math 20
Algebra and Multivariable
 Mathematics for Social
        Sciences
               Fall 2007

      http://my.harvard.edu/k19933
Léandra King
 leking@fas
               Matthew Leingang
                leingang@math
                                  Steven Stelmach
                                   stelmach@fas
Get to Know Indiana




“The Crossroads of America”
Hatsumon
Assignment
Decisions
        ©Michael Bretherton
Diet
4244.jpg
Migration
Data
The Objects
The Modeling Process
Real World               Mathematical
             Formulate
 Problem                    Model




                              Solve
  Test




Real World               Mathematical
               Predict
Prediction               Conclusion
Conceive
   Multiple
Dimensions
Model
Solve
Optimize
Diagonalize
Apply
Course
Business
Homework
Exams
Grade
                               93   A
                               90   A-
           Midterm I
Homework
             20%
                               87   B+
  25%


                               83    B
                               80   B-
              Midterm II
                 25%
   Final
                               75   C+
   30%


                               70   C
                               65   C-
                               50   D
Textbook
FAQ
See you next time

More Related Content

More from Matthew Leingang

Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Matthew Leingang
 
Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Matthew Leingang
 
Lesson 27: Integration by Substitution (handout)
Lesson 27: Integration by Substitution (handout)Lesson 27: Integration by Substitution (handout)
Lesson 27: Integration by Substitution (handout)Matthew Leingang
 
Lesson 26: The Fundamental Theorem of Calculus (handout)
Lesson 26: The Fundamental Theorem of Calculus (handout)Lesson 26: The Fundamental Theorem of Calculus (handout)
Lesson 26: The Fundamental Theorem of Calculus (handout)Matthew Leingang
 
Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)Matthew Leingang
 
Lesson 25: Evaluating Definite Integrals (handout)
Lesson 25: Evaluating Definite Integrals (handout)Lesson 25: Evaluating Definite Integrals (handout)
Lesson 25: Evaluating Definite Integrals (handout)Matthew Leingang
 
Lesson 24: Areas and Distances, The Definite Integral (handout)
Lesson 24: Areas and Distances, The Definite Integral (handout)Lesson 24: Areas and Distances, The Definite Integral (handout)
Lesson 24: Areas and Distances, The Definite Integral (handout)Matthew Leingang
 
Lesson 24: Areas and Distances, The Definite Integral (slides)
Lesson 24: Areas and Distances, The Definite Integral (slides)Lesson 24: Areas and Distances, The Definite Integral (slides)
Lesson 24: Areas and Distances, The Definite Integral (slides)Matthew Leingang
 
Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Matthew Leingang
 
Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Matthew Leingang
 
Lesson 22: Optimization Problems (slides)
Lesson 22: Optimization Problems (slides)Lesson 22: Optimization Problems (slides)
Lesson 22: Optimization Problems (slides)Matthew Leingang
 
Lesson 22: Optimization Problems (handout)
Lesson 22: Optimization Problems (handout)Lesson 22: Optimization Problems (handout)
Lesson 22: Optimization Problems (handout)Matthew Leingang
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Matthew Leingang
 
Lesson 21: Curve Sketching (handout)
Lesson 21: Curve Sketching (handout)Lesson 21: Curve Sketching (handout)
Lesson 21: Curve Sketching (handout)Matthew Leingang
 
Lesson 20: Derivatives and the Shapes of Curves (slides)
Lesson 20: Derivatives and the Shapes of Curves (slides)Lesson 20: Derivatives and the Shapes of Curves (slides)
Lesson 20: Derivatives and the Shapes of Curves (slides)Matthew Leingang
 
Lesson 20: Derivatives and the Shapes of Curves (handout)
Lesson 20: Derivatives and the Shapes of Curves (handout)Lesson 20: Derivatives and the Shapes of Curves (handout)
Lesson 20: Derivatives and the Shapes of Curves (handout)Matthew Leingang
 
Lesson 19: The Mean Value Theorem (slides)
Lesson 19: The Mean Value Theorem (slides)Lesson 19: The Mean Value Theorem (slides)
Lesson 19: The Mean Value Theorem (slides)Matthew Leingang
 
Lesson 18: Maximum and Minimum Values (slides)
Lesson 18: Maximum and Minimum Values (slides)Lesson 18: Maximum and Minimum Values (slides)
Lesson 18: Maximum and Minimum Values (slides)Matthew Leingang
 
Lesson 17: Indeterminate forms and l'Hôpital's Rule (slides)
Lesson 17: Indeterminate forms and l'Hôpital's Rule (slides)Lesson 17: Indeterminate forms and l'Hôpital's Rule (slides)
Lesson 17: Indeterminate forms and l'Hôpital's Rule (slides)Matthew Leingang
 
Lesson 18: Maximum and Minimum Values (handout)
Lesson 18: Maximum and Minimum Values (handout)Lesson 18: Maximum and Minimum Values (handout)
Lesson 18: Maximum and Minimum Values (handout)Matthew Leingang
 

More from Matthew Leingang (20)

Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)
 
Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)
 
Lesson 27: Integration by Substitution (handout)
Lesson 27: Integration by Substitution (handout)Lesson 27: Integration by Substitution (handout)
Lesson 27: Integration by Substitution (handout)
 
Lesson 26: The Fundamental Theorem of Calculus (handout)
Lesson 26: The Fundamental Theorem of Calculus (handout)Lesson 26: The Fundamental Theorem of Calculus (handout)
Lesson 26: The Fundamental Theorem of Calculus (handout)
 
Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)
 
Lesson 25: Evaluating Definite Integrals (handout)
Lesson 25: Evaluating Definite Integrals (handout)Lesson 25: Evaluating Definite Integrals (handout)
Lesson 25: Evaluating Definite Integrals (handout)
 
Lesson 24: Areas and Distances, The Definite Integral (handout)
Lesson 24: Areas and Distances, The Definite Integral (handout)Lesson 24: Areas and Distances, The Definite Integral (handout)
Lesson 24: Areas and Distances, The Definite Integral (handout)
 
Lesson 24: Areas and Distances, The Definite Integral (slides)
Lesson 24: Areas and Distances, The Definite Integral (slides)Lesson 24: Areas and Distances, The Definite Integral (slides)
Lesson 24: Areas and Distances, The Definite Integral (slides)
 
Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)
 
Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)
 
Lesson 22: Optimization Problems (slides)
Lesson 22: Optimization Problems (slides)Lesson 22: Optimization Problems (slides)
Lesson 22: Optimization Problems (slides)
 
Lesson 22: Optimization Problems (handout)
Lesson 22: Optimization Problems (handout)Lesson 22: Optimization Problems (handout)
Lesson 22: Optimization Problems (handout)
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)
 
Lesson 21: Curve Sketching (handout)
Lesson 21: Curve Sketching (handout)Lesson 21: Curve Sketching (handout)
Lesson 21: Curve Sketching (handout)
 
Lesson 20: Derivatives and the Shapes of Curves (slides)
Lesson 20: Derivatives and the Shapes of Curves (slides)Lesson 20: Derivatives and the Shapes of Curves (slides)
Lesson 20: Derivatives and the Shapes of Curves (slides)
 
Lesson 20: Derivatives and the Shapes of Curves (handout)
Lesson 20: Derivatives and the Shapes of Curves (handout)Lesson 20: Derivatives and the Shapes of Curves (handout)
Lesson 20: Derivatives and the Shapes of Curves (handout)
 
Lesson 19: The Mean Value Theorem (slides)
Lesson 19: The Mean Value Theorem (slides)Lesson 19: The Mean Value Theorem (slides)
Lesson 19: The Mean Value Theorem (slides)
 
Lesson 18: Maximum and Minimum Values (slides)
Lesson 18: Maximum and Minimum Values (slides)Lesson 18: Maximum and Minimum Values (slides)
Lesson 18: Maximum and Minimum Values (slides)
 
Lesson 17: Indeterminate forms and l'Hôpital's Rule (slides)
Lesson 17: Indeterminate forms and l'Hôpital's Rule (slides)Lesson 17: Indeterminate forms and l'Hôpital's Rule (slides)
Lesson 17: Indeterminate forms and l'Hôpital's Rule (slides)
 
Lesson 18: Maximum and Minimum Values (handout)
Lesson 18: Maximum and Minimum Values (handout)Lesson 18: Maximum and Minimum Values (handout)
Lesson 18: Maximum and Minimum Values (handout)
 

Recently uploaded

NewBase 19 April 2024 Energy News issue - 1717 by Khaled Al Awadi.pdf
NewBase  19 April  2024  Energy News issue - 1717 by Khaled Al Awadi.pdfNewBase  19 April  2024  Energy News issue - 1717 by Khaled Al Awadi.pdf
NewBase 19 April 2024 Energy News issue - 1717 by Khaled Al Awadi.pdfKhaled Al Awadi
 
Innovation Conference 5th March 2024.pdf
Innovation Conference 5th March 2024.pdfInnovation Conference 5th March 2024.pdf
Innovation Conference 5th March 2024.pdfrichard876048
 
Call Us 📲8800102216📞 Call Girls In DLF City Gurgaon
Call Us 📲8800102216📞 Call Girls In DLF City GurgaonCall Us 📲8800102216📞 Call Girls In DLF City Gurgaon
Call Us 📲8800102216📞 Call Girls In DLF City Gurgaoncallgirls2057
 
Ten Organizational Design Models to align structure and operations to busines...
Ten Organizational Design Models to align structure and operations to busines...Ten Organizational Design Models to align structure and operations to busines...
Ten Organizational Design Models to align structure and operations to busines...Seta Wicaksana
 
Flow Your Strategy at Flight Levels Day 2024
Flow Your Strategy at Flight Levels Day 2024Flow Your Strategy at Flight Levels Day 2024
Flow Your Strategy at Flight Levels Day 2024Kirill Klimov
 
Call US-88OO1O2216 Call Girls In Mahipalpur Female Escort Service
Call US-88OO1O2216 Call Girls In Mahipalpur Female Escort ServiceCall US-88OO1O2216 Call Girls In Mahipalpur Female Escort Service
Call US-88OO1O2216 Call Girls In Mahipalpur Female Escort Servicecallgirls2057
 
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
8447779800, Low rate Call girls in Uttam Nagar Delhi NCRashishs7044
 
Global Scenario On Sustainable and Resilient Coconut Industry by Dr. Jelfina...
Global Scenario On Sustainable  and Resilient Coconut Industry by Dr. Jelfina...Global Scenario On Sustainable  and Resilient Coconut Industry by Dr. Jelfina...
Global Scenario On Sustainable and Resilient Coconut Industry by Dr. Jelfina...ictsugar
 
Cybersecurity Awareness Training Presentation v2024.03
Cybersecurity Awareness Training Presentation v2024.03Cybersecurity Awareness Training Presentation v2024.03
Cybersecurity Awareness Training Presentation v2024.03DallasHaselhorst
 
Intro to BCG's Carbon Emissions Benchmark_vF.pdf
Intro to BCG's Carbon Emissions Benchmark_vF.pdfIntro to BCG's Carbon Emissions Benchmark_vF.pdf
Intro to BCG's Carbon Emissions Benchmark_vF.pdfpollardmorgan
 
APRIL2024_UKRAINE_xml_0000000000000 .pdf
APRIL2024_UKRAINE_xml_0000000000000 .pdfAPRIL2024_UKRAINE_xml_0000000000000 .pdf
APRIL2024_UKRAINE_xml_0000000000000 .pdfRbc Rbcua
 
Kenya’s Coconut Value Chain by Gatsby Africa
Kenya’s Coconut Value Chain by Gatsby AfricaKenya’s Coconut Value Chain by Gatsby Africa
Kenya’s Coconut Value Chain by Gatsby Africaictsugar
 
IoT Insurance Observatory: summary 2024
IoT Insurance Observatory:  summary 2024IoT Insurance Observatory:  summary 2024
IoT Insurance Observatory: summary 2024Matteo Carbone
 
Call Girls in DELHI Cantt, ( Call Me )-8377877756-Female Escort- In Delhi / Ncr
Call Girls in DELHI Cantt, ( Call Me )-8377877756-Female Escort- In Delhi / NcrCall Girls in DELHI Cantt, ( Call Me )-8377877756-Female Escort- In Delhi / Ncr
Call Girls in DELHI Cantt, ( Call Me )-8377877756-Female Escort- In Delhi / Ncrdollysharma2066
 
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCRashishs7044
 
Buy gmail accounts.pdf Buy Old Gmail Accounts
Buy gmail accounts.pdf Buy Old Gmail AccountsBuy gmail accounts.pdf Buy Old Gmail Accounts
Buy gmail accounts.pdf Buy Old Gmail AccountsBuy Verified Accounts
 
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...ShrutiBose4
 
8447779800, Low rate Call girls in Tughlakabad Delhi NCR
8447779800, Low rate Call girls in Tughlakabad Delhi NCR8447779800, Low rate Call girls in Tughlakabad Delhi NCR
8447779800, Low rate Call girls in Tughlakabad Delhi NCRashishs7044
 
8447779800, Low rate Call girls in Kotla Mubarakpur Delhi NCR
8447779800, Low rate Call girls in Kotla Mubarakpur Delhi NCR8447779800, Low rate Call girls in Kotla Mubarakpur Delhi NCR
8447779800, Low rate Call girls in Kotla Mubarakpur Delhi NCRashishs7044
 
Market Sizes Sample Report - 2024 Edition
Market Sizes Sample Report - 2024 EditionMarket Sizes Sample Report - 2024 Edition
Market Sizes Sample Report - 2024 EditionMintel Group
 

Recently uploaded (20)

NewBase 19 April 2024 Energy News issue - 1717 by Khaled Al Awadi.pdf
NewBase  19 April  2024  Energy News issue - 1717 by Khaled Al Awadi.pdfNewBase  19 April  2024  Energy News issue - 1717 by Khaled Al Awadi.pdf
NewBase 19 April 2024 Energy News issue - 1717 by Khaled Al Awadi.pdf
 
Innovation Conference 5th March 2024.pdf
Innovation Conference 5th March 2024.pdfInnovation Conference 5th March 2024.pdf
Innovation Conference 5th March 2024.pdf
 
Call Us 📲8800102216📞 Call Girls In DLF City Gurgaon
Call Us 📲8800102216📞 Call Girls In DLF City GurgaonCall Us 📲8800102216📞 Call Girls In DLF City Gurgaon
Call Us 📲8800102216📞 Call Girls In DLF City Gurgaon
 
Ten Organizational Design Models to align structure and operations to busines...
Ten Organizational Design Models to align structure and operations to busines...Ten Organizational Design Models to align structure and operations to busines...
Ten Organizational Design Models to align structure and operations to busines...
 
Flow Your Strategy at Flight Levels Day 2024
Flow Your Strategy at Flight Levels Day 2024Flow Your Strategy at Flight Levels Day 2024
Flow Your Strategy at Flight Levels Day 2024
 
Call US-88OO1O2216 Call Girls In Mahipalpur Female Escort Service
Call US-88OO1O2216 Call Girls In Mahipalpur Female Escort ServiceCall US-88OO1O2216 Call Girls In Mahipalpur Female Escort Service
Call US-88OO1O2216 Call Girls In Mahipalpur Female Escort Service
 
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
 
Global Scenario On Sustainable and Resilient Coconut Industry by Dr. Jelfina...
Global Scenario On Sustainable  and Resilient Coconut Industry by Dr. Jelfina...Global Scenario On Sustainable  and Resilient Coconut Industry by Dr. Jelfina...
Global Scenario On Sustainable and Resilient Coconut Industry by Dr. Jelfina...
 
Cybersecurity Awareness Training Presentation v2024.03
Cybersecurity Awareness Training Presentation v2024.03Cybersecurity Awareness Training Presentation v2024.03
Cybersecurity Awareness Training Presentation v2024.03
 
Intro to BCG's Carbon Emissions Benchmark_vF.pdf
Intro to BCG's Carbon Emissions Benchmark_vF.pdfIntro to BCG's Carbon Emissions Benchmark_vF.pdf
Intro to BCG's Carbon Emissions Benchmark_vF.pdf
 
APRIL2024_UKRAINE_xml_0000000000000 .pdf
APRIL2024_UKRAINE_xml_0000000000000 .pdfAPRIL2024_UKRAINE_xml_0000000000000 .pdf
APRIL2024_UKRAINE_xml_0000000000000 .pdf
 
Kenya’s Coconut Value Chain by Gatsby Africa
Kenya’s Coconut Value Chain by Gatsby AfricaKenya’s Coconut Value Chain by Gatsby Africa
Kenya’s Coconut Value Chain by Gatsby Africa
 
IoT Insurance Observatory: summary 2024
IoT Insurance Observatory:  summary 2024IoT Insurance Observatory:  summary 2024
IoT Insurance Observatory: summary 2024
 
Call Girls in DELHI Cantt, ( Call Me )-8377877756-Female Escort- In Delhi / Ncr
Call Girls in DELHI Cantt, ( Call Me )-8377877756-Female Escort- In Delhi / NcrCall Girls in DELHI Cantt, ( Call Me )-8377877756-Female Escort- In Delhi / Ncr
Call Girls in DELHI Cantt, ( Call Me )-8377877756-Female Escort- In Delhi / Ncr
 
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
 
Buy gmail accounts.pdf Buy Old Gmail Accounts
Buy gmail accounts.pdf Buy Old Gmail AccountsBuy gmail accounts.pdf Buy Old Gmail Accounts
Buy gmail accounts.pdf Buy Old Gmail Accounts
 
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
 
8447779800, Low rate Call girls in Tughlakabad Delhi NCR
8447779800, Low rate Call girls in Tughlakabad Delhi NCR8447779800, Low rate Call girls in Tughlakabad Delhi NCR
8447779800, Low rate Call girls in Tughlakabad Delhi NCR
 
8447779800, Low rate Call girls in Kotla Mubarakpur Delhi NCR
8447779800, Low rate Call girls in Kotla Mubarakpur Delhi NCR8447779800, Low rate Call girls in Kotla Mubarakpur Delhi NCR
8447779800, Low rate Call girls in Kotla Mubarakpur Delhi NCR
 
Market Sizes Sample Report - 2024 Edition
Market Sizes Sample Report - 2024 EditionMarket Sizes Sample Report - 2024 Edition
Market Sizes Sample Report - 2024 Edition
 

Math 20 Introduction