Math 1a
 
Freshman Mathematics
Fall 2014-15
 
MWF 10:00 //  Baxter Lecture Hall 
Course Description | Policies | Textbooks | Lecture Notes | Handouts | Homework | Sections

Instructor:  Nets Katz , 266 Sloan, 626-395-4326, nets@caltech.edu

Instructor's Office Hours:  Thursday 5 PM -6 PM Sunday 9 PM - 10 PM

Lead TA: Foo Yee Yeo, 385 Sloan, 626-395-1732, fyeo@caltech.edu

Course Secretary:   Kathy Carreon , 253 Sloan, 626-395-4335, kcarreon@caltech.edu


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How to choose tracks of Math 1b ::: In case you missed it how to choose tracks If I were interested in taking 108a next year, I would pick analytical. I'm talking to you: ACM majors.






Sections


Section 2

TA: Daniel Siebel 155 Sloan, ext.4081

Office Hours: Saturday 5pm, 155 Sloan

Recitation

9:00AM Thursday

11 DWN (Downs)

 

Section 3:

TA:Connor Meehan, 156 Sloan, ext. 6805

Office Hours: Sunday 5pm, 159 Sloan

Recitation

9:00AM Thursday

103 DWN (Downs)

 

Section 4:

TA: Ruiyuan Ronnie Chen, 382 Sloan, 4366

Office Hours: Sunday 11 A.M., 382 Sloan

Recitation

10:00AM Thursday

257 SLN (Sloan)

 

Section 5:

TA: Peter Burton, 156 Sloan, ext 6805

Office Hours: Sunday 6pm, 159 Sloan

Recitation

10:00AM Thursday

27 GTS (Gates)

 

Section 6:

TA:Seunghee Ye, 160 Sloan, ext 4324

Office Hours: Sunday 8pm, 160 Sloan

Recitation

10:00AM Thursday

11 DWN (Downs)

 

Section 8:

TA: Xiang Ni, 353 Sloan, ext. 1731

Office Hours: Saturday 9 A.M., 353 Sloan

Recitation

1:00PM Thursday

103 DWN (Downs)

 

Section 9:

TA: Emad Nasrollapoursamami, 160 Sloan, ext 4324

Office Hours: Friday 7pm, 160 Sloan

Recitation

1:00PM Thursday

22 GTS (Gates)

 

Section 10: Lead TA

TA: fyeo@caltech.edu, 385 Sloan, ext 1732

Office Hours: Friday 8pm, 385 Sloan

Recitation

2:00PM Thursday

142 Kck (Keck)

 

Section 11:

TA:Gahye Jeong, 155 Sloan, ext 4081

Office Hours: Saturday 10am, 155 Sloan

Recitation

2:00PM Thursday

119 DWN (Downs)

 

Section 12:

TA: Siqi He, 155 Sloan, ext 4081

Office Hours: 7:00 P.M. Saturday

Recitation

2:00PM Thursday

103 DWN (Downs)

 

 

 

 

Course Description
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This course will introduce the mathematical method through (One Variable) Calculus. By the mathematical method, what we primarily mean is the ability to express one's self with absolute precision, and then to use logical proofs to establish that certain precise statements are universally true. We assume that the Caltech freshman has reasonable familiarity with single variable calculus as a computational system, but we emphasize explaining, or testing, why things work and how to justify one's propositions. In Ma 1a, the underlying concepts will be stressed, as well as the need for checking the hypotheses precisely as to where the results apply. A main focus will be on the writing of complete proofs so the case one is making is ironclad and unassailable. It will emerge that when we do this, we actually know more than the standard computational aspects of single variable calculus and that we can answer questions which are new to us and come up naturally once all the terms in Calculus are carefully defined and the definitions used. Some of these questions are also quite natural from the point of view of the scientist and engineer.

The topics listed below will be treated during the Fall quarter:

  • Mathematical induction and the real number system.
  • Sequences and Series
  • Continuous Functions
  • Differential Calculus
  • Integral Calculus
  • Polynomial Approximations
  • L'Hopital's rule for 0/0
  • Improper Integrals
  • Complex Numbers
  • Integral Tests, Abel summation for series

Policies
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Homework:

Homework is due Mondays at 10 AM and will be posted on the course website on Tuesday the previous week. All problems may be done in collaboration with others. However, each student must write down the solution in his or her own individual way and there should be no two identical solutions to any problem. Do not consult the solution sets from previous years in working this year's problem.

At most one late homework set will be accepted throughout the quarter, and only at your TA's discretion. Arrangements must be made in advance with your TA, and the homework set in question must be submitted no later than Wednesday 10 a.m. of the same week. Beyond this, late homework will NOT be accepted, without a letter from the Infirmary or from the Dean (or Associate Dean). Every week, graded homework can be picked up from the TA during the recitation on Thursday.

Grading and Exams:

There will be weekly assignments, as well as a Midterm and a Final examination, each of the Take Home variety lasting three hours. The final grade (of P or F) will depend on a composite of these factors. To be precise, the homework will be worth 40 percent, while the final and midterm will be worth 30 percent. No one will be excused from the final exam.

The use of calculators, computer software, homework assignments and solution sets from previous terms, books and notes and or other such tools is NOT permitted on the exams. Collaboration on exams is not allowed.

Collaboration is allowed on the homework but you must write the solutions in your own language. Use of books and notes is allowed on the homework but you may not use solution sets from previous terms if they do the exact same problems. Use of calculators and computer software is allowed for homework but you are encouraged (unless software is specifically mentioned in the homework) to only use these tools to check your work.

Recitations:

Please go to the recitations! Each week, a portion of the recitation will be dedicated to introducing some computational (or even theoretical) aspect which the Instructor will not have time to present in class. In general, get to know your TA and bug him/her to death (figuratively speaking) with your questions, and try to fill in all the holes in your understanding. Don't wait till the midterm to start doing that.

Extra Help: Tutoring is available for anyone who feels they would benefit from some extra assistance.

Office Hours:

Instructor and TA office hours will be posted very soon. 


Textbooks
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Calculus Volume 1, Tom M. Apostol ISBN 0-471-00005-1
Official course lecture notes, under construction Nets Hawk Katz This has the problems for your problem sets

Last year's Lecture Notes


Date Description

September

Lecture 1: Induction and the natural numbers

October

Lecture 2: The real numbers

October

Lecture 3: Limits

October

Lecture 4: Cauchy sequences, Bolzano-Weierstrass, and the squeeze theorem

October

Lecture 5: Infinite series

October

Lecture 6: Power series ::: Addendum: Limit Laws

October

Lecture 7: Limits and Continuity

October

Lecture 8: The derivative: local theory

October

Lecture 9: The mean value theorem

October

Lecture 10: Application of the mean value theorem

October

Lecture 11: Exponentiation

October

Lecture 12: Formal Power Series

November

Lecture 13: Inverses

November

Lecture 14: The Riemann Integral

November

Lecture 15: Integration and Uniform Continuity

November

Lecture 16: The fundamental theorem of Calculus

November

Lecture 17: Numerical Integration

November

Lecture 18: Taylor's approximation revisited

November

Lecture 19: Arclength and trig functions

November

Lecture 20: Convexity and Optimization

November

Lecture 21: Inequalities

November

Lecture 22: Macroeconomics

November

Lecture 23: Complex numbers

November

Lecture 24: Roots of Polynomials

December

Lecture 25: Analytic functions

December

Lecture 26: Cauchy's Theorem

December

Lecture 27: Taylor Series for analytic functions.

Dinakar Ramakrishnan's Notes (as a reference)
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Date Description


Chapter 0


Chapter 1


Chapter 2


Chapter 3


Chapter 4


Chapter 5


Chapter 6


Chapter 7


Chapter 8


Chapter 9

Handouts
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Date Description



Problem Sets
 

Due Date Problem Set  Solutions

October 6

Problem Set 1

 

October 13

Problem Set 2

 




October 20

Problem Set 3

 



October 27

Problem Set 4

 


November 3 (just kidding)

Practice problems


November 10

Problem Set 5

 


November 17

Problem Set 6

 


November 24

Problem Set 7

 


December 3

Problem Set 8

 



Practice problems for the final

     
     


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