Instructor: Mark Sing

Office: Kassar 012

Email: mark_sing@brown.edu

Pronouns: she/her, they/them

Masks are required

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:

- Functions and modeling with functions
- Polynomials and power series
- Continuity and limits
- Derivatives and their calculation
- Differential equations and the fundamental theorem of the derivative
- Discrete and polynomial approximation
- Exponential and logarithmic functions
- 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:

- the study of functions by their growth
- the development of tools for approximating functions
- a mathematical framework for modeling processes in physics, chemistry, engineering, and more

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:

- 3 hours of lecture
- 1 hour of recitation
- 2 hours reading/reviewing your notes and the lecture notes
- 6 hours of homework

Homework is crucial to success in this course. All assignments are

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

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.

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:

- 40% Midterm
- 10% Final Exam
- 50% Homework

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:

- Make a reasonable attempt at the problem on your own first
- Mention who you worked with and cite your sources
- 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

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

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

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.

Week 1: 9/6, 9/8 | |||||
---|---|---|---|---|---|

Recitation | Tuesday | Thursday | |||

no recitation!! | no class!! | First class. Syllabus and bottle calibration. (notes) |
|||

worksheet | 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 | solutions | worksheet | solutions | ||

Week 3: 9/20, 9/22 | |||||

Recitation | Tuesday | 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 | |||

Exponential functions - definition and properties.
(notes) |
Wrapping up exponential functions
(notes) |
||||

worksheet | worksheet | solutions | worksheet | solutions | |

solutions | homework | solutions | homework | solutions | |

Week 7: 10/18, 10/20 | |||||

Recitation | Tuesday | Thursday | |||

Recap of derivative rules and a new rule (composition).
Higher derivatives and nonlinear derivatives. Composition rule. (notes) |
Inverse functions and their derivatives. Examples and practice.
(notes) |
||||

worksheet | worksheet | solutions | worksheet | solutions | |

solutions | homework | solutions | homework | solutions | |

Week 8: 10/25, 10/27 | |||||

Recitation | Tuesday | Thursday | |||

Several perspectives on the logarithm.
(notes) |
More on the logarithm and its properties.
(notes) |
||||

worksheet | worksheet | solutions | worksheet | solutions | |

solutions | homework | solutions | homework | solutions | |

Week 9: 11/1, 11/3 | |||||

Recitation | Tuesday | Thursday | |||

Differential equations and approximation. Integration.
(notes) |
Differential equations and the fundamental theorem of the derivative.
(notes) |
||||

worksheet | worksheet | solutions | worksheet | solutions | |

solutions | homework | solutions | homework | solutions | |

Week 10: 11/8, 11/10 | |||||

Recitation | Tuesday | Thursday | |||

No recitation. | No class. | Differential equations
(notes) |
|||

worksheet | solutions | ||||

homework | solutions | ||||

Week 11: 11/15, 11/17 | |||||

Recitation | Tuesday | Thursday | |||

Trigonometry
(notes) |
Trig identities made easy
(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. | |||

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 | |

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.

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