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Math Xa Introduction to Functions and Calculus

Math Xa Introduction to Functions and Calculus . Fall 2008 Introductory Meeting John Hall. High School. Consumer of Knowledge Teacher shows you how to do it. Harvard. Producer of Knowledge Teacher guides you, but you do a lot of work on your own. Quote.

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Math Xa Introduction to Functions and Calculus

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  1. Math XaIntroduction to Functions and Calculus Fall 2008 Introductory Meeting John Hall

  2. High School • Consumer of Knowledge • Teacher shows you how to do it.

  3. Harvard • Producer of Knowledge • Teacher guides you, but you do a lot of work on your own.

  4. Quote • “Merely accumulating information is of little value to students. Facts are soon forgotten, and the sheer volume of information has grown to the point that it is impossible to cover all the important material or even to agree on what is most essential. Concepts and theories have little value unless one can apply them to new situations.” • -Derek Bok, Former President of Harvard University

  5. About Math Xa • The development of calculus by Newton and Leibniz ranks among the greatest achievements of the past millennium.

  6. About Math Xa • Learning to see the world through the lens of mathematics • Communicating this mathematical point of view to others through speech, writing, and graphics • Using the mathematics of change to make decisions and predictions about the world

  7. Is Math Xa For Me? • Yes, if you are unsure of your precalculus skills (trig, logs, exponentials, etc). • Likely, if you haven’t had calculus. Most of the students in 1a have already had calculus

  8. How We Teach Math X • Class on M,W,F will involve some interactive lecture, discussions, group work, and your participation. • Mandatory weekly workshops on Monday or Tuesday will help you learn to solve challenging problems and give you a chance to work with your peers. • Course assistants will lead problem sessions.

  9. Course Requirements • Homework • Two midterms and a final exam • Algebra test • Weekly workshops on Monday/Tuesday

  10. Homework • Skill problems due each class period, problem sets due once a week. • Part of our goal is teaching mathematical communication; your work should provide complete explanations and be easy to read. • You will receive comments on your homework, but no numerical scores. Your homework grade will be based on how many problems you complete correctly. • If you do not correctly complete a problem in a problem set, you will be allowed to resubmit that problem together with the following week’s problem set. If the second solution is complete and correct, you will receive full credit for the problem. • Look on the website for the up-to-date homework assignments.

  11. Exams • Midterms: Monday 11/3 from 7-9 pm and Monday 12/8 from 7-9 pm. • Calculators are not allowed. • Final Exam in January.

  12. Algebra Test • Algebra pre-test on Monday, September 29, 7-8 pm. See course website for more information. • Algebra post-test on Wednesday, October 15, 7-8 pm (we will keep the highest score). • Problem sessions will offer algebra help.

  13. Workshops • Weekly 90-minute Workshops will be led by a former Math X student. • Problems will be challenging - often on the level of difficult exam problems. The entire group will solve the problems together. • The focus is on learning to solve problems rather than on getting the right answer.

  14. Problem Sessions • In college, expect your math classes to focus on theory, understanding, and developing new material, not on training you to complete homework and exams. • Problem session is a resource to help you learn technical skills and problem solving.

  15. Calculators • Any graphing calculator will be helpful. • If you would like to buy one, we recommend a TI-84, TI-86, or a TI-89. • Calculators will be allowed on homework but not on exams.

  16. Textbook • Calculus: An Integrated Approach to Functions and Their Rates of Change, by Robin Gottlieb • Available as a course packet for $40 from FlashPrint (99 Mt. Auburn St.)

  17. Course Topics • Functions: graphs, inverses, transformations • Differentiation: rates of change, linear approximations to functions, optimization • Differential Equations

  18. Grading • Homework: 20% • Algebra Test: 10% • Workshop Attendance: 5% • Midterm I: 20% • Midterm II: 20% • Final Exam: 25%

  19. Getting Help with Math Xa • Other Xa students. • CA problem session • TF Office Hours • The Math Question Center (8:30 pm - 10:30 pm Sunday through Thursday)

  20. Advising • Math advising hours can be found at: http://www.math.harvard.edu/sectioning/

  21. Sectioning • Math Xa is taught in small sections. • You must section by 12:30 pm on Wednesday, September 17th. • Sectioning directions are on: http://www.math.harvard.edu/sectioning/

  22. Your Homework • The Bottle Calibration Problem. • Due the first day of class. • Read syllabus carefully!

  23. Bottle Calibration Problem • Height of liquid in this bottle is a function of the volume of liquid in the bottle • We can represent this function by a graph

  24. Important Emails • John Hall (Course Head) hall@math.harvard.edu • Juliana Belding (Assistant Course Head) jbelding@math.harvard.edu

  25. Math XaIntroduction to Functions and Calculus • Fall 2007 Introductory Meeting • John Hall • Why attend Harvard? • i.e. What should you expect from you tuition money? • High School • Consumer of Knowledge • Teacher shows you how to do it. • At Harvard • Producer of Knowledge • Teacher guides you, but you do a lot of work on your own. • General Relativity • Polio Vaccine • Real Estate • Quote • “Merely accumulating information is of little value to students. Facts are soon forgotten, and the sheer volume of information has grown to the point that it is impossible to cover all the important material or even to agree on what is most essential. Concepts and theories have little value unless one can apply them to new situations.” • -Derek Bok, Former President of Harvard University • About Math Xa • The development of calculus by Newton and Leibniz ranks among the greatest achievements of the past millennium. • About Math Xa • Learning to see the world through the lens of mathematics • Communicating this mathematical point of view to others through speech, writing, and graphics • Using the mathematics of change to make decisions and predictions about the world • Is Math Xa For Me? • Yes, if you are unsure of your precalculus skills (trig, logs, exponentials, etc). • Likely, if you haven’t had calculus. Most of the students in 1a have already had calculus • How We Teach Math X • Class on M,W,F will involve some interactive lecture, discussions, group work, and your participation. • Course assistants will lead problem sessions. • Weekly workshops on Monday or Tuesday will help you learn to solve challenging problems and give you a chance to work with your peers. • Course Requirements • Homework • Two midterms and a final exam • Algebra test • Weekly workshops on Monday/Tuesday • Homework • Generally due each class period. • Part of our goal is teaching mathematical communication, so your work should provide explanations and be easy to read. • Some problems will be written in paragraph form. • Please work with your peers, but write up your own solutions. • Look on the website for the up-to-date homework assignments. • Exams • Midterms: Monday 11/5 from 7-9 pm and Monday 12/10 from 7:30-9:30 pm. • Calculators are not allowed. • Final Exam in January. • Algebra Test • Algebra pre-test on Monday, October 1, 7-8 pm. See course website for more information. • Algebra post-test on Monday, October 15, 6-7 pm (we will keep the highest score). • Algebra Workshop on Friday from 3-5 pm in SC Hall A. • Problem sessions will offer algebra help. • Workshops • Weekly 90-minute Workshops will be led by a former Math X student. • Problems will be challenging -- often on the level of difficult exam problems. The entire group will solve the problems together. • The focus us on learning to solve problems rather than getting the right answer. • Problem Sessions • In college, expect your math classes to focus on theory, understanding, and developing new material, not on training you to complete homework and exams. • Problem session is a resource to help you learn technical skills and problem solving. • The text • Online notes • Calculators • Any graphing calculator will be helpful. • If you would like to buy one, we recommend a TI-84, TI-86, or a TI-89. • Calculators will be allowed on homework but not on exams. • Course Topics • Functions: graphs, inverses, transformations • Differentiation: rates of change, linear approximations to functions, optimization • Grading • Homework: 20% • Algebra Test: 10% • Workshop Attendance: 5% • Midterm I: 20% • Midterm II: 20% • Final Exam: 25% • Getting Help with Math Xa • Other Xa students. • CA problem session • TF Office Hours • The Math Question Center (MQC) in SC B-10 (8:30 pm - 10:30 pm Sunday through Thursday) • Advising • Math advising hours can be found at: http://www.math.harvard.edu/sectioning/index.html • Sectioning • Math Xa is taught in small sections. • You must section by 1:00 pm on Wednesday, September 19th. • Sectioning directions are on: http://www.math.harvard.edu/sectioning/index.html • Your Homework • The Bottle Calibration Problem. • Due the first day of class. • Read syllabus online • Bottle Calibration Problem • Height of liquid in this bottle is a function of the volume of liquid in the bottle • We can represent this function by a graph • Important Emails • Bret Benesh (Course Head) • benesh@math.harvard.edu • John Hall (Assistant Course Head) hall@math.harvard.edu

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