Math 51 Syllabus
Fall 2025

Course:   Math 51, Calculus I ( Course Catalog)

Course Description:

An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. This sequence is intended for majors in engineering and the physical sciences.

Throughout this course, students will engage in problem-solving and critical thinking activities designed to strengthen their analytical skills and mathematical intuition. As a prerequisite for many programs in science, engineering, and mathematics, calculus provides an essential foundation for understanding the principles of change and motion in the physical world. Students will not only develop proficiency with core calculus concepts but also learn to recognize and apply them in scientific and real-world contexts, thereby deepening their mathematical insight and understanding.

Credit Hours:  4  

(Students will receive no credit for Math 51 after completing Math N1A, Math 16B, Math N16B, or XMATH 1A. A deficient grade in Math 51 may be removed by taking Math N1A. )

Prerequisites:  

Three and one-half years of high school math, including trigonometry and analytic geometry. Contact the Mathematics Department for details. Students with AP credit should consider choosing a course more advanced than Math 51.

Course Learning Objectives: 

After successfully completing this course, you'll be able to:



• Demonstrate understanding of the basic concepts of one-variable calculus including those of limits, continuity, derivatives, and integration.


• Recognize how and when these mathematical ideas and methods can be applied in other disciplines.


• Differentiate between technical mathematical results and their interpretations in applications.

Textbook: 

The required textbook for the course is Stewart, Single Variable Calculus: Early Transcendentals for UC Berkeley 8th edition (ISBN: 9781305765276, Cengage).


• This is a custom edition containing chapters 1-9, 11 and 17 of Stewart's "Calculus: Early Transcendentals", 8th edition. The regular edition is also fine, it just contains extra chapters covered in math 53. We'll cover material in chapters 1-6.


• I strongly encourage you to read the textbook regularly throughout the semester. It provides a level of detail that cannot be fully addressed in lectures, and developing this habit will be essential for your academic progress. The homework exercises are drawn directly from the text, and studying the examples carefully will clarify the methods needed to approach and solve them.

Homework:  

Homework assignments will be announced on the Homework page.


• Homework is to be submitted to Gradescope generally on Friday by 11:59 pm (Pacific Time). Here are instructions for how to upload your work.


• In order to accomodate for unforeseen technical difficulties, we will accept homework submitted within 24 hours from the due date without a penalty.


• There will be 14 problem sets. Your cumulative homework grade will be based on the best 12 of the 14.


• In view of the above arrangement, NO late homework will be accepted.


• If you have issues submitting your work, contact your GSI promptly.


• Assignments will be evaluated on two components: completeness (3 points) for submitting all problems, and correctness (3 points) based on one randomly selected problem.


• You can work on the problems with your classmates, but you must write down your own version. Copying solutions from others is not accepted and is considered cheating.


• A good portion of the quizzes and exams will be based on the weekly problem sets. So it is extremely important for you to make sure that you understand each one of them.

Discussion sections and Quizzes:

Discussion sections take place MWF or TuTh depending on your enrollment. You are required to attend the discussion section that you are enrolled in. If you need to switch discussion sections, then please contact enrollment@math.berkeley.edu. We (the instructor and GSIs) have no influence on the enrollment process.

Quizzes will take place during your discussion sections, roughly once every two weeks.


• Quizzes will be on Wednesdays and Thursdays depending on your discussion section.


• Your cumulative quiz grade will be based on the best 5 of the 7.


• There will be no makeup quizzes. If a student misses a quiz for any reason, it will be counted as 0.


• Each quiz will last about 15 minutes and be closely related to the homework from the previous two weeks.


• The quiz schedule is available on the Calendar page.


• To ensure fairness across all discussion sections, you are not allowed to share quiz content or solutions with classmates until after Friday of the same week.

Exams: 

There will be two midterm exams and a final exam. Exams will be in-person.




• Midterm 1 is scheduled for Tuesday, September 30 (during lecture)


• Midterm 2 is scheduled for Tuesday, November 4 (during lecture)


• Final Exam for LEC 001 is scheduled for Tuesday, December 16, 3 pm (Location: Wheeler 150)


• Final Exam for LEC 002 is scheduled for Wednesday, December 17, 3 pm (Location: Wheeler 150)


• Please check the announcment on bCourses for more details regarding the final exam.


It is your responsibility to make sure that you do not have any scheduling conflicts with the exams. There will be no make-up exams. As per university policy, if you do not sit the final exam, you automatically fail the course. Please check the dates now to make sure that you have no unavoidable conflicts.




• Cheatsheets will not be allowed for the exams.


• No calculators or electronic devices of any kind will be allowed for the examinations.


• Please bring your student ID to the exam.


• Academic Integrity violations will be taken seriously, and will be reported to higher authorities for disciplinary action.

Grading:

There are two methods to determine your course grade:


• Method 1:   12% Homework (Best 12 out of 14),   10% Quizzes (Best 5 out of 7),   20% Midterm 1,   20% Midterm 2,   38% Final Exam


• Method 2:   12% Homework (Best 12 out of 14),   10% Quizzes (Best 5 out of 7),  28% Better Midterm,   50% Final Exam


Your grade will be computed using both methods and then the better grade will be used to determine your course grade.

Your final letter grade will be based on your ability to demonstrate a solid understanding of the material and to apply it effectively across a wide range of problems. Broadly, the following criteria describe the level of mastery typically associated with each letter range:


• A-/A/A+: Central concepts are thoroughly understood; computational techniques (including subtleties) are mastered and applied accurately across a diverse set of problems; strong ability to connect abstract concepts to a variety of real-world applications.


• B-/B/B+: Central concepts are generally well understood, though minor misunderstandings may be present; core computational techniques are reasonably well understood (though subtleties may be lacking) and applied fairly accurately to many problems; some ability to connect abstract concepts to real-world contexts.


• C-/C/C+: Central concepts are only partially understood, with major misunderstandings; core computational techniques are poorly understood and applied reliably only in very standard cases; limited ability to connect abstract concepts to even basic real-world applications.


Final grade cutoffs will be determined once the course is complete, but you will receive feedback on your standing after each midterm. To ensure fairness, historic class averages will also be considered. This means that if an exam turns out to be unusually difficult, that will be reflected in the final grade distribution.

Please note that external considerations-such as the need for a particular grade for admission or retention in an academic program, scholarship eligibility, transfer credit, graduation requirements, or personal preference-are not included in the grade calculation and therefore do not affect your final course grade. While effort, improvement, attendance, and participation are valuable and can greatly enhance your performance on exams, they are not directly factored into the numerical determination of your course grade.

Students who have substantially completed the course but for serious extenuating circumstances, are unable to complete the remaining course activities, may request an Incomplete grade. This request must be submitted in writing to the GSI and instructor. You must provide verifiable documentation for the seriousness of the extenuating circumstances. Refer to the Office of the Registrar's website for more information on the university's policy on Incomplete Grades.

Accommodations:

If you require course accommodations due to a physical, emotional, or learning disability, contact UC Berkeley's Disabled Students' Program (DSP). Notify the instructor and GSI through course email of the accommodations you would like to use. You must have a Letter of Accommodation on file with UC Berkeley to have accommodations made in the course. UC Berkeley is committed to providing robust educational experiences for all learners. With this goal in mind, we have enabled the ALLY tool for this course. You can now automatically generate "Alternative Formats" for course files and bCourses Pages. Depending on the context, these formats can include Tagged PDF, HTML, BeeLine Reader, Electronic Braille, ePub, Immersive Reader, MP3, and translated versions. For more information, watch the video entitled, "Ally Tutorial for Students at UC Berkeley.""


Questions about your DSP accommodations:
• HW and Quizzes: Contact your GSI in advance.
• Exams: We will make sure that you can take advantage of the extended time for midterm and final exams as specified in your Letter of Accommodation. This means that you can either take your midterm or final exam with the DSP proctoring service or that we will provide an additional room where you can take your exam. We will provide more information later. If you want to take advantage of any accommodation beyond this, then please contact the Head GSI at least one week before each exam. The Head GSI will arrange for your DSP exams and contact you with the arrangements.
• If the issues are not resolved, contact the professor.

Regrades:

Regrade requests will be made using the built-in regrade request feature in Gradescope. There will be a limited window of time after your graded work is made available during which the regrade request feature will be active. This time window will be announced when the scores are released to the students. Please be advised that the regrade request window is usually brief, and if you want to request a regrade, it is your responsibility to make the request during the allowed time. Please understand that while we will correct errors in the grading, we will not modify the grading rubric or negotiate over partial credit after graded papers are returned to students.

ED discussion:

The GSIs, the Head GSI, and I will be offering help on Ed Discussion. Monday-Friday.

Only comments/questions pertaining to the mathematical content of the course are allowed. Any postings that do not meet this criteria will be deleted and EDdiscussion privileges may be removed. As a diverse community of learners, students must strive to work together in a setting of civility, tolerance, and respect for each other and for the instructor. Conflicting opinions among members of a class are to be respected and r esponded to in a professional manner. There are to be no offensive comments or language.

Late Add Policy:

If you are on the waitlist for a course, you are expected to attend class and complete assignments. If a student does not attend class or does not turn in assignments before the due dates, the student will receive a 0 on all missed assignments. No exceptions will be made. Similarly, a student not on a waitlist who adds the class late will not be given additional time, nor will they be excused from the assigned work.

Academic Integrity:

Academic integrity is a cornerstone of scholarship at UCB. Upholding honesty in your work reflects your personal values and sustains the trust essential to our academic community. Acts of dishonesty undermine these principles and may lead to serious consequences under university policy, including administrative sanctions such as suspension or expulsion. By committing to integrity, you help foster a fair and meaningful learning environment for yourself and others. For more information about university policies on academic integrity, check UC Berkeley Center for Student Conduct.

Use of GenAI Tools:

In this course, our goal is to support your active learning, knowledge building, and development of critical thinking skills. To ensure that you get the most out of these experiences, we ask that you do not use GenAI tools or automated services to complete homework, quizzes, or exams. Unless a specific assignment explicitly allows their use, you must refrain from using GenAI (or other online tools) for any part of your work. This helps ensure that the work you submit truly reflects your own understanding and growth. If the use of AI/online tools is suspected, the instructor may ask you to complete a brief follow-up (oral or written) to confirm your understanding of the material. In cases where this is not possible, a zero may be given for that assignment.

Rules regarding absences and missed exams, assignments, etc.:

Attendance in class or in the discussion section (for exams or quizzes) is highly recommended, but not required. If you miss a class, then you can catch up by watching the Course Capture recordings. If you miss a discussion section, then we recommend asking a classmate for the missed material. If you miss one of the midterm exams (for example due to illness or an athletic trip), then your course grade will be computed using grading method 2. We will also drop a few of the lowest quiz and homework grades. These rules will be applied automatically and you do not need to inform us about your absences.

We are aware that a number of students will miss a midterm exam, quiz or a homework assignment due to a variety of reasons. This is why we have implemented generous replacement or dropping rules. The purpose of these rules is precisely to alleviate the impact of such absences. So we will not be able to offer further accommodations like make-up exams or further drops. If you think that these rules did not fully cover your absences, then you can email us at the end of the semester and we will review your case.

The only exception to the above is if you have an official Letter of Accommodation issues by the DSP office and that requests accommodation for missed exams or if your absence is related to your DSP accommodations (your DSP specialist will need to verify this with us). In this case, please contact us and we will try to find an arrangement.

Please do not share doctor's notes with us or any other documents containing private information. For privacy reasons we cannot ask for doctor's notes. Therefore, we also cannot accept them for equity reasons. Otherwise your classmates would be forced to release private information in order to receive the same accommodations. The only document that we accept is your official Letter of Accommodation issued by the DSP office.

Practical Study Advice:


• Teach to Learn : One of the most effective ways to master a topic is to teach it. Try explaining the material to a classmate, a family member, or a friend. Anticipate the questions they might ask -- it is a great way to check your understanding and identify any gaps in your knowledge.
• Master the Details : True understanding comes from paying attention to the finer points. A superficial understanding of a topic is not sufficient; success comes from noticing the subtleties and understanding how they show up in problem-solving.
• Invest Your Time : Success in this course requires consistent effort. A 4-unit class typically translates to about 12 hours of work per week-time that will help you keep up with material, practice skills regularly, and deepen your understanding. Think of this time as an investment in mastering the subject.
• Practice for Success : The practice exams are one of the most important parts of your preparation. I will provide three practice exams for each test, and they will be fairly challenging. The main exam will contain close variations of these problems, and without serious practice it will feel much harder. By exam day, you should be able to solve all practice problems perfectly and unprompted. Start working on them at least a week in advance.

External Support:


• For questions about enrollment, contact Marsha Snow or email enrollment@math.berkeley.edu.


• The Student Learning Center provides support for this class, including full adjunct courses, review sessions for exams, and drop-in tutoring. You can find more details about Math 51 support here .


• If you struggle with a more basic principle (for example the power laws or another prerequisite for this class), then it may be a good idea to review this principle first before trying to solve a more advanced problem. You can review a basic principle by watching the corresponding video in Foundations of Lower Divisions Mathematics (created by Alexander Paulin) or by enrolling for Math 1 to review the basic prerequisites for Math 51.