Math 1a
 
Freshman Mathematics
Fall 2011 - 12
 
MWF 10:00 - 10:55 AM // Baxter Lecture Hall 
Course Description | Policies | Textbooks | Lecture Notes | Handouts | Homework | Sections

Instructor:  Matilde Marcolli, 162 Sloan, 626-395-4324, matilde@caltech.edu

Office Hours:   By appointment

Lead TA:  Michel van Garrel, 304 Kellogg, 626-395-4027, garrel@caltech.edu

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


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Sections


Section 2
TA:Kevin Teh

Office Hours: Tuesday, 12/06 1pm 156 Sloan

Recitation:

9:00 a.m., Thursday,

159 Sloan

 

Section 3 -
TA:Melissa Yeung

Office Hours: Monday, 12/05, 10am

SFL Mutimedia Conference Room 328

Recitation:

9:00 a.m., Thursday,

103 Downs

 

Section 4 -
TA:Michel van Garrel (Lead TA)

Office Hours: Sunday, 12/04 6pm 304 KEL

Recitation:

10:00 a.m., Thursday,

159 Sloan

 

Section 5 -
TA:Ross Elliot

Office Hours: Monday, 12/05 Noon 356 Sloan

Recitation:

10:00 a.m., Thursday,

11 Downs

 

Section 6 -
TA: Liubomir Chiriac

Office Hours: Monday, 12/05 3pm 260 Sloan

Recitation:

10:00 a.m., Thursday,

119 Downs

 

Section 7 -
TA: Laura Peskin

Office Hours: Saturday, 12/03 2pm, 260 Sloan

Recitation:

1:00 p.m., Thursday,

107 downs

 

Section 8 -
TA:Robin Tucker-Drob

Office Hours: Monday, 12/05 5pm, 156 Sloan

Recitation:

1:00 p.m., Thursday,

22 Gates

 

Section 9 -
TA:Michel van Garrel (Lead TA)

Office Hours: Sunday, 12/04 6pm 304 KEL

Recitation:

1:00 p.m., Thursday,

3 BBB (Bechman Lab)

 

Section 10 -
TA:Brian Skinner

Office Hours: Saturday, 12/03 4pm 256 Sloan

Recitation:

2:00 p.m., Thursday,

103 Downs

 


 

 

 

 

 

 

Course Description
  Top

This course will introduce the mathematical method through (One Variable) Calculus, with which the Caltech freshman has reasonable familiarity, at least for doing calculations (assuming various results as black boxes). The typical high school courses, and the AP tests themselves, are woefully inadequate in explaning, 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. Learning to think precisely and rationally will come in handy in life, regardless of which subject one majors in.

The first nine topics below, and as much as possible of the tenth topic, will be treated during the Fall quarter:

  • Introduction to writing proofs, using the 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 web site on Tuesday of the previous week. The first homework will be posted on the second week of class. All problems may be done in collaboration with others. However, each student must write down the solution in his/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 Monday 10 a.m. of the following week. Beyond this, late homework will NOT be accepted, without a letter from the Infirmary or from the Dean (or Associate Dean). Late homework should be handed either to the course secretary or to your TA. 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 facotrs. To be precise, the homework will be worth 50 percent, the midterm 20 percent and the final 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 homework but you must write the solutions in your own language. Use of books and notes is allowed on 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 untill the midterm to start doing that.

Extra Help: Tutoring is available for anyone who feels they would benefit from some extra assistance.It is provided by the Deans and is free of charge. To take advantage of it, refer to the above link.

Office Hours:

Instructor and TA office hours will be posted very soon. 


Textbooks
  Top

Calculus Volume 1, Tom M. Apostol ISBN 0-471-00005-1

Lecture Notes

These notes are from the previous year and are a useful complement to the class. They do not cover all content of the class, nor in the same order.

Course Capture  Top


Date Description
9/28/11 week 1 - Proofs in Mathematics
9/28/11 week 2 - The Real Number System
9/28/11 week 3 - Sequences and Series
9/28/11
week 4 - Limits of functions, Continuity
9/28/11 week 5 - Differential Calculus
9/28/11 week 6 - Integration
9/28/11 week 7 - Fundamental Theorems, Substitution, Integration by Parts, and Polar Coordinates
9/28/11 week 8 - Improper Integrals, Exp, Log, Arcsin, and the Integral Test for Series
9/28/11
week 9 - Approximations, Taylor Polynomials, and Taylor Series
9/28/11
week 10 - Complex numbers and functions, Factoring, and integration by parts

Expanded Notes
These notes are for enrichment. The covered topics do not appear in class  Top

 

Date Description
9/28/11
week 2 - The Number System: An expanded treatment (D. Ramakrishnan)
9/28/11 week 3 - Sequences and Series (D. Ramakrishnan)
9/28/11 week 8 - Calculus and Economics (K. Border)
9/28/11
week 9 - Stirling's formula (B. Simon)

Handouts
  Top

Date Description



Homework
  Top

Due Date Homework  Solutions
Mon. 10/10/11 @ 10 am Set 1  
Mon. 10/17/11 @ 10 am Set 2  
Mon. 10/24/11 @ 10 am Set 3  
Mon. 11/07/11 @ 10 am Set 4  
     
Mon. 11/14/11 @ 10 am Set 5  
Mon. 11/21/11 @ 10 am Set 6  
WED. 11/30/11 @ 10 am Set 7 updated 11/23/11
   


 
     
     
     


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