Math 50: Analytic Geometry and Calculus


Contact

Instructor: Mark Sing (they/them)
Office: Kassar 012
Office Hours: Kassar 205, Monday 2:00-3:30 (Mark); Zoom, Wednesday afternoons (Mark, by appointment); and Sayles 306 Sunday and Wednesday 5:00-6:00 (Phoebe)
Email: mark_sing@brown.edu and phoebe_dragseth@brown.edu


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. Discrete and polynomial approximation
  6. Exponential and logarithmic functions
  7. Extrema and optimization

Course Structure

Each week there will be two lectures (TR 2:30 - 3:50pm) and one recitation (R 4:00-4:50pm).

To help organize the material and your learning, most lessons are structured around a worksheet (mainly adapted from those of Professor Yu-Wen Hsu). During the lesson there will be some lecture but most time spent will be working on the problems from the worksheets in small groups, guided by the instructor. Groups will be asked to explain their work and questions to each other.

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


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. And you are always welcome to come to office hours with questions!!

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 on the course website. Homework will typically be released Fridays and Mondays, and due during class on Tuesday and Thursday (sometimes moved slightly to accommodate holidays and exams).

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 to let them know that you won't be able to finish the homework on time and to work out an alternative time to submit your assignment (ideally within a week of the original due date).


Exams

There will be one midterm exam and one final exam. Tentatively, the first exam will fall in Week 8, 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. The breakdown of your grade will be as follows:


Academic Integrity and Collaboration Policy

Academic Integrity and Collaboration Policy} We take academic integrity very seriously. Our goal, above everything 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, but we ask that you write and submit your own solutions, rather than copying those of other students. The best way to follow this policy is to start problems on your own and work until you get stuck before consulting others for help you finish. Violation of this policy, cheating on exams, or any other form of academic dishonesty is prohibited by Brown’s Academic Code and may have serious consequences.


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, 9/16.

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.

Here is a link to the final project

Week 1: 9/7, 9/9
Tuesday Thursday Recitation
no class!! First class. Syllabus and bottle calibration. no recitation!!
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 2: 9/14, 9/16
Tuesday Thursday Recitation
All about functions!! Linear, absolute value, quadratic, square root, polynomials. Domain, range, and graphs.
(notes)
Transformations of functions and graphs.
(notes)
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 3: 9/21, 9/23
Tuesday Thursday Recitation
More on transformations of functions and graphs.
(notes)
Approximations by lines and polynomials. Formalism of power series. Decimal numbers and limits. The virial equation of state.
(notes)
no recitation
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 4: 9/28, 9/30
Tuesday Thursday Recitation
Limits and rational functions.
(notes)
First look at the derivative as ``best linear approximation''.
(notes)
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 5: 10/5, 10/7
Tuesday Thursday Recitation
More practice with derivatives. Approximation.
(notes)
Derivative rules (sum, product, quotient).
(notes)
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 6: 10/12, 10/14
Tuesday Thursday Recitation
Exponential functions - definition and properties.
(notes)
Further practice with exponential functions. Recap of derivative rules and one new rule (composition).
(notes)
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 7: 10/19, 10/21
Tuesday Thursday Recitation
Wrapping up exponential functions: they really are exponential.
(notes)
Polynomial approximations from rate equations. Inverse functions.
(notes)
no recitation
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 8: 10/26, 10/28
Tuesday Thursday Recitation
More on inverse functions and their derivatives. Examples. Several perspectives on the logarithm.
(notes)
More on the logarithm and its properties.
(notes)
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 9: 11/2, 11/4
Tuesday Thursday Recitation
Exam review!!!! Exam!!!!
Practice Exam solutions exam solutions
Study Guide

Week 10: 11/9, 11/11
Tuesday Thursday Recitation
Discuss midterm. Assign final project. Begin optimization, and increasing/decreasing functions.
(notes)
More on optimization, with examples. Connection to quadratic approximation. Second derivative test.
(notes)
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 11: 11/16, 11/18
Tuesday Thursday Recitation
More practice with optimization, rate equations.
(notes)
Wrapping up optimization/additional topics.
(notes)
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 12: 11/24, 11/26
Tuesday Thursday Recitation
no class no class no recitation

Week 13: 11/30, 12/2
Tuesday Thursday Recitation
Additional topics (???)
(notes)
Additional topics (???)
(notes)
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions

Week 14: 12/7, 12/9
Tuesday Thursday Recitation
Additional topics (???)
(notes)
Final project presentations.
(notes)
no recitation
worksheet solutions worksheet solutions worksheet
homework solutions homework solutions solutions


Miscellaneous

Most of my past students have enjoyed seeing my bunny, Cujo, so a few photos are attached here. He makes a welcome break from mathematics for me, and I hope for you as well!!

Cujo occasionally visits my office - I'll send out email in advance if you'd like to meet him (only if you are not allergic to rabbits or hay!!)

Cujo standing in front of a brick wall.
Cujo standing on his back legs next to a box of hay.
Cujo sitting at the top of his cardboard house and looking down.
Cujo lying down and sleeping under my desk.
Cujo's friend Peter, a different rabbit

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