Math 50: Analytic Geometry and Calculus



Contact

Instructor: Mark Sing
Office: Kassar 012
Office Hours: T 4:00-5:00 and Zoom by appointment
Email: mark_sing@brown.edu
Pronouns: she/her, they/them




Course Description

Together, Math 50 and Math 60 cover the calculus material in Math 90, as well as review of the necessary precalculus topics. My goal is for you to leave this course with both solid mathematical knowledge in precalculus and single variable calculus, as well as a strong conceptual understanding of the material to apply it to future courses you take here.

A brief list of topics we aim to cover:

  1. Functions and modeling with functions
  2. Polynomials and power series
  3. Continuity and limits
  4. Derivatives and their calculation
  5. Differential equations and the fundamental theorem of the derivative
  6. Discrete and polynomial approximation
  7. Exponential and logarithmic functions
  8. Extrema and optimization

Calculus is a multifaceted subject, and we will aim to thoroughly explore it from several angles. Here are some of our guiding definitions of calculus:

  1. the study of functions by their growth
  2. the development of tools for approximating functions
  3. a mathematical framework for modeling processes in physics, chemistry, engineering, and more
Both the practical and theoretical aspects of calculus manifest in different ways in each of these. This is not a proof-based course, so we will draw heavily on examples and intuition to motivate the theory. However, where it is reasonable and helps your understanding, we may sketch some computational proofs.


Course Structure

Each week there will be two 80 minute lectures (TR 2:30 - 3:50pm) and one 50 minute recitation (T 12:00 - 12:50pm).

To help organize the material and your learning, most lessons are structured around a worksheet. During the lesson there will a combination of lecture, group work, and class discussion revolving around the worksheet, guided by the instructor.

The format of recitations is similar, but it will have no lecture and include no new material.

You should expect to work at least 12 hours a week for this course, roughly broken down as follows:


Homework

Homework is crucial to success in this course. All assignments are mandatory.
It is nearly impossible to learn and master any course without spending time working on problems. The only way to learn math is by doing math!! Homework will usually be slightly different than problems discussed in class; presenting the material in different contexts will help you develop a more flexible understanding.

Each homework set is short and two are due each week to ensure you are continuously engaging with the material without overwhelming your schedule. Problem sets and their due dates will be posted to the calendar on this course website (see below). Homework will typically be released Fridays and Mondays, and due during class on Tuesday and Thursday (sometimes moved slightly to accommodate holidays and exams). In the calendar, each assignment appears under the day it is due.

Homework grading will emphasize conceptual understanding and a willingness to put effort into the assignment.

Late homework will be accepted with no penalty but we ask that you email the instructor in advance (when possible) to let them know and arrange an alternative time of way to submit your assignment (ideally within a week of the original due date).


Exams

There will be a take home midterm exam and a take home final example. Tentatively, the first exam will fall in Week 11-12, and the final exam during the usual final exam period. The final exam is not cumulative.


Grading

Math 50 is only offered on an S/NC basis. Assignments are graded on a combination of effort and correctness, and we will always provide ample opportunities for revision if you are concerned about a particular grade. The breakdown of your grade will be as follows:


Academic Integrity and Collaboration Policy

Our goal, above all else, is that you work hard and learn the material as well as you are able.

You are strongly encouraged to work together on your homework assignments, and may also consult other sources, including the internet, but with three small stipulations:

  1. Make a reasonable attempt at the problem on your own first
  2. Mention who you worked with and cite your sources
  3. Always write up the solutions in your own words, and be sure you understand and internalize any steps that were explained to you by someone else
For purely computational problems, I ask that you do not use symbolic calulators like WolframAlpha or Mathematica, simply because that defeats the purpose. You are more than welcome to compare with your classmates or use those tools only to check your answers.

Another good resource is the Math Resource Center, available four nights a week with TAs who can answer your questions.


Calendar and Files

Here is our course calendar and all the files (class notes, worksheets, homework assignments, and solutions). Each day also has a brief description of the topics covered.

In this calendar, the homework file is located at day it is due. For instance, the homework file in Thursday of Week 2 is due on that Thursday, 9/15.

Homework due Tuesday will be posted the Friday before, and homeworks due on Thursday will be posted on the Monday before. Typically, homework due on Thursday will include concepts from Tuesday's class, so skimming it ahead of time might be useful!

Topics, especially for later weeks, are subject to change. Some of the unmarked days are specifically for extra topics chosen by student interest.

You may also view all the notes as one file, especially convenient for printing.


(notes)
Week 1: 9/6, 9/8
Recitation Tuesday Thursday
no recitation!! no class!! First class. Syllabus and bottle calibration.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 2: 9/13, 9/15
Recitation Tuesday Thursday
no recitation!! All about functions!! Linear, absolute value, quadratic, square root, polynomials, rational. Domain, range, and graphs.
(notes)
Transformations of functions and graphs.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 3: 9/20, 9/22
RecitationTuesday Thursday
More on transformations of functions and graphs.
(notes)
Approximations by lines and polynomials. Decimal numbers and limits.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 4: 9/27, 9/29
Recitation Tuesday Thursday
Limits and Big O notation.
Squiggle notation.
(notes)
Limits and approximation.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 5: 10/4, 10/6
Recitation Tuesday Thursday
First look at the derivative as ``best linear approximation''.
Fundamental Theorem of the derivative.
(notes)
More practice with derivatives. Derivative rules (sum, product, quotient).
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 6: 10/11, 10/13
Recitation Tuesday Thursday
More on derivatives. The square root.
(notes)
Approximations and sketching.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 7: 10/18, 10/20
Recitation Tuesday Thursday
Exponential functions - definition and properties.
(notes)
Composition rule.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 8: 10/25, 10/27
Recitation Tuesday Thursday
FTD and e^(rx), e^(a+x)
(notes)
Differentiation review.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 9: 11/1, 11/3
Recitation Tuesday Thursday
Differentiation review.
(notes)
Higher and nonlinear derivatives. Inverse functions and the logarithm.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 10: 11/8, 11/10
Recitation Tuesday Thursday
No recitation. No class. Polynomial approximation.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 11: 11/15, 11/17
Recitation Tuesday Thursday
Polynomial Approximation Polynomial Approximation.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 12: 11/22, 11/24
Recitation Tuesday Thursday
No recitation. No class. Midterm! No class.
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 13: 11/29, 12/1
Recitation Tuesday Thursday
Optimization and approximation.
(notes)
More on optimization.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions

Week 14: 12/6, 12/8
Recitation Tuesday Thursday
Additional topics.
(notes)
Additional topics.
(notes)
worksheet worksheet solutions worksheet solutions
solutions homework solutions homework solutions


Miscellaneous

Most of my past students have enjoyed seeing my bunnies, Cujo & Lula (brown and grey, respectively), so a few photos are attached here. They make a welcome break from mathematics for me, and I hope for you as well!!

The bunnies occasionally visit my office - think of them as extra TAs.

Cujo and Lula napping together in front of a brick wall.
Cujo's friend Peter, a different rabbit

This is Cujo & Lula's friend Peter, whose friend David contributed to the design of this website. Thanks!