MA 511-601 Spring 2026

Advanced Calculus I Course Syllabus

Department of Mathematics · NC State University

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Table of Contents

Course Information

How to Reach Me

Even though the course is asynchronous and online, I enjoy interacting with students and want you to feel comfortable contacting me throughout the semester. Please read the section below for the best way to reach me:

Course Description

(3 credit hours) Fundamental theorems on continuous functions; convergence theory of sequences, series and integrals; the Riemann integral. Credit for both MA 425 and MA 511 is not allowed.

Prerequisite. MA 341. MA 225 is desirable but not required.

Learning Objectives

MA 511 is an introduction to mathematical analysis. Upon successful completion of this course, students will be able to:

  1. Explain the foundational concepts of real analysis, including set theory basics, limits, completeness, continuity, differentiability, integrability, and convergence of functions and sequences.

  2. Construct clear and rigorous mathematical proofs, using common methods such as direct proof, contradiction, contrapositive, and induction, with attention to logical structure and written clarity.

  3. Apply theorems precisely and appropriately to analyze and compare the behavior of sets, sequences, functions, and series in one-variable calculus.

  4. Interpret and connect definitions and major results in analysis to support problem-solving and deeper conceptual understanding.

  5. Communicate mathematical arguments effectively, demonstrating fluency with the language, notation, and conventions of analysis.

We will focus some attention on learning to write mathematical proofs. Proofs will be graded not only for content but also for writing and style. (A mathematically correct proof which is poorly written may receive a low grade.)

Course Structure

In general this course will consist of three interactive video lectures per week with a weekly quiz, written homework assignments (approximately every two weeks), and three tests.

Lecture Materials

Our lectures are contained in H5P modules on Moodle. During each lecture activity, you will be asked the equivalent of “in-class quiz questions.” These questions do not count towards your course grade, but give you a way to assess how well you are following the lecture. My hope is that you will find that the questions highlight major concepts and improve your understanding–they were written to guide you, not to test you. Some of these questions pop-up automatically, while others must be clicked on (typically look for a purple indicator or open circle both on the slides and along the progress bar).

I recommend you only begin a lecture if you can fully commit your attention to it. Note that you can pause and return at a later time. You can also speed up the pace of the lecture (up to 2x speed).

You must complete the lecture summary questions to see the Moodle quiz covering lecture material. Thus I recommend that you try to complete all lectures by each Friday at the latest.

Each lecture has slides and bookmarks to allow you to quickly reach content you wish to review.

You may watch the videos directly in YouTube if you prefer. However, you must answer the pop-up questions in Moodle to get points to unlock the weekly quizzes. Thus you should not exclusively watch the course content in YouTube.

Student Choice Lecture

The required lectures cover the fundamental ideas of real analysis on ℝ.

Since many students who take MA 511 are graduate students in other disciplines, you may be interested in applying real analysis in various situations. Thus I have prepared eight additional topics from the textbook.

Throughout the semester, you must choose one of these “Student Choice” lectures. You will watch the lecture and complete the required assignment–there will be no examination questions on these topics. These lectures have been interspersed throughout the weeks based on when they are most relevant to the required material; however, the activity is not due until the end of the last week of class. Here is a list of these topics, together with my recommendations:

Choose one of the lectures below and complete its assignment by the end of the semester. The "Recommended for" column notes typical audiences and any prerequisites.

Table: Chart of Student Choice Lectures

Section Title Recommended for those interested in...
2.3 Markov Chains Statistics / Probability; Economics (requires linear algebra / eigen theory)
2.7 Quadratic Map General math — Dynamical Systems
Posted supplement Compact Sets General math — Analysis and Topology
4.4 Newton's Method Math education
5.4 Integral Equations General math — Differential Equations
5.5 Calculus of Variations General math — Analysis
10.1 Discrete Random Variables Statistics / Probability
10.2 Coding Theory Statistics / Probability; Computer Science


If you see a section or topic in a Real Analysis I/Advanced Calculus I book which has not been mentioned but which piques your interest, you may request a different topic before the last month of class. I will see if the topic is suitable and prepare an activity for you (or you can suggest good problems!).

Communication and Getting Help

Forum

We will use Piazza for class discussion and homework questions. You are encouraged to use Piazza to discuss concepts and homework with discretion-hints and suggestions are okay, but full solutions will be deleted. You can post under your name or you may be anonymous to your classmates; however, the instructor will be able to see who you are. Please be respectful of your fellow classmates' ideas and attempts. If you have a math question you are not sure should be a public post, it is better to send me a direct message as a private post on Piazza.

Enroll in this class Piazza through the Piazza link near the top of Moodle.

Request: when asking a question about a specific item (like an item in Moodle), please include a direct link to that item (e.g. the Moodle url). It helps everyone answer your question a lot faster.

Email

Please be sure to see the beginning of this syllabus for the best ways to contact me.

Contact me for confidential and private discussions about grades, scheduling office hours, etc. Please include MA 511 in the subject line. In general, I may not respond to messages outside of business hours (M-F, 9am-5pm), and it may take 24-72 hours for me to respond to an message. Math questions are generally best asked in office hours or on our forum, not by email.

Homework

There are two types of homework in this class: Moodle quizzes (completed entirely in Moodle) and written homework (submitted to the grading platform Gradescope through Moodle). You are responsible for tracking quiz and homework due dates.

Quizzes

There are weekly ∼45-minute quizzes on Moodle which become available following completion of the lectures. Quizzes will require you to demonstrate knowledge of definitions and theorems. You may be asked to provide specific statements and will be evaluated based on correct and precise wording; using a computer is likely more convenient than using a phone for the quizzes. Although the quizzes are open notes/open book, your success in the course is closely linked to your familiarity with the terminology–heavy dependence during the quizzes on notes/books is discouraged.

On most quizzes you have two attempts per problemand one overall submission (so do not submit the entire quiz until you are done with each question). If your first attempt on a question is not correct, you can click on your answer and reattempt the question.

You can start a quiz, answer a few questions, close your browser, and resume later on a different device. You do not need to complete the quiz in one sitting. You also do not need to formally “submit” the quiz–Moodle will submit it on your behalf at the deadline.

Written Homework

Homework assignments in real analysis are often challenging and lengthy. You should begin working on them as soon as possible. All homework assignments are posted on Moodle and are due by 11pm (Eastern) on the listed day. Homework will be submitted through Gradescope.

On each homework assignment, you may work in a group (up to 4... 2-3 is ideal). Let me know if you would like to be introduced to other classmates looking for a group, or you can reach out to everyone on Piazza. If you work in a group, be sure to declare all members with the submission by clicking this button: (and only one person should submit).

Test Information

There will be three “midterm” examinations–the final exam is Midterm 3. The exams each test about one third of the course. While they are not written to test earlier material deliberately, as the course progresses some questions will naturally rely on your mastery of earlier topics.

Test Dates

Proctors

All examinations will be proctored through DELTA. You will either take your exam with DELTA, or coordinate remote proctoring with DELTA, according to which situation best describes you:

I encourage you to look through DELTA Testing Service's website, especially their frequently asked questions (FAQs).

Note: the word remote in this context means that you are using a professional testing site (for example, a testing center, a local library, a college, etc.) other than DELTA. Remote testing does not mean testing at home.

Please sign up your preferred time and date as soon as possible. Time slots fill up fast:

Your Final Exam Schedule On‑Campus Testing Off‑Campus Proctoring Reschedule with DELTA DELTA FAQs

You may reschedule an exam appointment directly with DELTA using the link above. You do not need to contact the instructor for permission, provided that your new appointment is scheduled within the exam's posted date range.

DELTA and exam links

Calculators

You may use scientific calculators on exams. These calculators must not have calculus capabilities (differentiation, integration), CAS (computer algebra system) capabilities, or access to the internet.

There are descriptions and examples of calculators here: Calculator Guidelines. If you are on-campus, you may rent a suitable calculator from the NC State Libraries: Calculator rentals at NC State Libraries.

Classroom Expectations

  1. Course Structure: This is an online class; you are responsible for your own learning and for pacing yourself within course guidelines.

    • Watch the video lectures scheduled each week and follow the Course Calendar.
    • Track all due dates in Moodle and on the Course Calendar.
    • Complete all assignments in a timely fashion.
    • Post your math questions in the course forum for discussions and Q&A.
    • Optional: attend live sessions.

  2. Communication and announcements: Please check your email, the course forum, and the Moodle site regularly. All announcements sent by email will also be saved under Announcements on Moodle. You are responsible for knowing the content of course emails.

  3. Respect and professionalism: Treat everyone in class (students and instructor) with respect and courtesy. Be active and prepared in any live sessions. Come to office hours ready to ask questions and communicate with others.

  4. Accountability: You are responsible for resolving any confusion about assignments, due dates, exams, accommodations, etc., in a prompt manner.

  5. Academic integrity: Do not submit work that is not yours. It is understood that your name on any assignment indicates your adherence to the NC State Honor Pledge: "I have neither given nor received unauthorized aid on this test or assignment."

  6. Exam device policy: Review the permitted items before each exam. Keep phones and other forbidden devices powered off and stored away during exams to avoid accidental use.

Student Success

Student well-being is important to success at NC State. Every student, faculty member, and staff member enriches the community through varied perspectives, knowledge, and experience. Our classroom should be a space where every student is respected and heard.

In an effort to affirm and respect the identities of all students in the classroom and beyond, please contact me if you wish to be referred to using a name and/or pronouns other than those listed in the student directory.

I welcome any suggestions you have for making our classroom more welcoming.

Grading

Grade Weighting and Numerical Conversion

Your grade will be determined by the following breakdown:

[1] Due to Moodle incorrectly storing some lecture scores, your lecture scores do not count towards your course grade. However, you are still expected to earn credit for each lecture to access the relevant quiz.

Grades are tracked in real-time in the Moodle Gradebook.

Conversion from Numerical Grade to Letter Grade

A student's numerical average will be converted to a letter grade as follows (do not expect any additional rounding, extra credit, or curves):

Standard Conversion Table
Grade Range
A+97-100
A93-96.99
A-90-92.99
B+87-89.99
B83-86.99
B-80-82.99
C+77-79.99
C73-76.99
C-70-72.99
D+67-69.99
D63-66.99
D-60-62.99
F0-59

Requirements for Credit-Only (S/U) Grading

In order to receive a grade of S, students are required to take all exams, complete all assignments, and earn a grade of C- or better. Conversion from letter grading to credit only (S/U) grading is subject to university deadlines. Refer to the Registration and Records calendar for deadlines related to grading. For more details refer to REG 02.20.15 - Credit-Only Courses.

It is the student's responsibility to check if an S grade gives progress towards their degree(s).

Requirements for Auditors (AU)

Information about and requirements for auditing a course can be found at REG 02.20.04 - Audits.

Policies on Incomplete Grades

NC State Policy

At the discretion of the instructor, students may be given an IN grade for work not completed because of a serious interruption in their work not caused by their own negligence. An IN must not be used, however, as a substitute for an F when the student's performance in the course is deserving of failing. An IN is only appropriate when the student's record in the course is such that the successful completion of particular assignments, projects, or tests missed as a result of a documented serious event would enable that student to pass the course.

If an extended deadline is not authorized by the instructor or department, an unfinished incomplete grade will automatically change to an F after either (a) the end of the next regular semester in which the student is enrolled (not including summer sessions), or (b) the end of 12 months if the student is not enrolled, whichever is shorter. Incompletes that change to F will count as an attempted course on transcripts. The burden of fulfilling an incomplete grade is the responsibility of the student. See the university policy on incomplete grades: REG 02.50.03 - Grades and Grade Point Average.

Course Schedule

The course schedule is tentative and subject to change. Adjustments may be made to accommodate the pace of the class and unforeseen circumstances. All major changes will be announced in class and posted on Moodle.

Important Dates

For holidays and other university closures, please consult the general NC State Academic Calendar.

Your final exam schedule is already determined; find it here: NC State Final Exam Calendar. You are responsible for reviewing your final exam sessions to arrange a suitable time for this course.

List of Topics

Here are the major topics of MA 511, with the approximate regular-semester time allocated to each:

Course Continuity

To ensure course continuity, changes made to the method of instructional delivery, course structure, course schedule, number of assignments, grading or other aspects of the course after the start of the term will be communicated to all students in written form (e.g., by an instructor announcement) when course changes are implemented.

Additional Information

Student Expenses

Recommended book

Not required: Fundamental Ideas of Analysis by Michael Reed, 1st edition. ISBN: 9780471159964.

We will cover all or parts of Chapters 1–6 and 9. Topics will be the real number system, functions and limits, topology on the real line, continuity, differential and integral calculus for functions of one variable, infinite series, uniform convergence, and Fourier series.

Optional Text Supplements

There are free online resources for learning Analysis I, and many students have completed MA 511 successfully without purchasing the textbook. In addition to the recommended book, you may find the following books helpful

I have linked to some useful texts in the Course Reserves (you can also find these on Moodle): NC State Library Course Reserves.

The first two chapters of Reed are also available in Course Reserves.

List of topics

The beginning of the course will slightly reorder some of the topics compared to Reed (mainly so that we introduce and use the Supremum Property as a foundational axiom). From Chapter 3 onwards, we will follow Reed’s ordering.

Relative to the optional book, the order of the sections will be: 1.1 (on your own), 1.4, 1.2, 2.5, 1.3, Supplement on open and closed sets, Supplement on the Cantor set, 2.1, 2.2, 2.4 & 2.6 (both in two lectures), 3.1, 3.2, 3.3 (two lectures), 3.5, 3.6, 4.1, 4.2 (two lectures), 4.5, 5.1 (two lectures), 5.2, 5.3, 5.6, 5.7, 6.2, 6.3, 6.4, 4.3, 9.1, 9.2, 9.3.

Late Assignments

If you are having a busy week, please let me know as occasional extensions are acceptable. Unless we have discussed an extension, late homework shall be accepted up to five days late with a penalty of 5% per day (e.g., turning a Monday assignment in on Wednesday incurs a 10% penalty, a Friday assignment handed in on Monday incurs a 15% penalty). Be sure to begin each assignment early.

In general, I will grant extensions of up to a week so long as they are requested in advance of the due date. If you find you repeatedly need extensions, then we should meet on Zoom to discuss how to work effectively in this course.

Assignments submitted later than two weeks passed the original due date will not be accepted.

To request an extension or other considerations due to extenuating circumstances, please work with NCSU Class Absence Verification; here is the link to that office: NC State Absence Verification Process

Submission Timing and Availability Policy

Assignments are due by 11:00 pm on the posted due date. I am happy to help with technical questions, but please note that I am generally only available for troubleshooting until 5:00 pm on due dates.

To reduce stress and avoid last-minute issues, I strongly encourage you to begin and finish your homework well before 5:00 pm. Starting early gives you time to ask questions and ensures that unexpected problems—such as internet outages or system issues—do not interfere with submitting your work on time.

Because last-minute technical problems are often unavoidable but difficult to resolve after hours, extensions cannot be granted for issues that arise in the evening. Moodle access logs are reviewed when extension requests are submitted, and if the logs show that the homework was first accessed on the due date, an extension will generally not be possible.

In short, planning ahead is the best way to protect your work and your grade. Summary:

For longer-term, recurring, or more serious illness or other interruptions to your participation in this class, you should reach out to your instructor as soon as you can.

Late Examinations

Excused absense. If an exam is missed with an excused absence (that is, for a university-approved reason with supporting documentation), then a make-up test will be scheduled individually. The make-up test may contain different questions and be assessed differently than the regular test. Documentation for an excused absence must be provided within 1 week of the missed class. All absences that require a make-up exam or other special accommodations must go through the NC State University absence verification process. Here is the link to that office: NC State Absence Verification.

Failure to schedule. You must schedule exams in a timely fashion to guarantee that you will be able to take them. It is the instructor’s discretion whether a make-up exam will be allowed if you are not able to schedule an exam appointment within the selected time frame. If the instructor approves a make-up exam, there may be a 10% penalty on that exam. The make-up test may contain different questions and be assessed differently than the regular test.

Other absences. If an exam is missed for an unexcused absence, that exam will be given a score of 0.

Attendance

Since this course is an asynchronous online course, there is no daily attendance. Instead, each student's participation in Moodle is tracked to check for regular activity. For complete attendance and excused absence policies, please see Attendance Regulations (NCSU REG 02.20.03).

Academic Integrity

Students are required to comply with the university policy on academic integrity found in the Code of Student Conduct (NCSU POL11.35.01). Your submission of any exam indicates "I have neither given nor received unauthorized aid on this test or assignment." Violations of academic integrity will be handled in accordance with the Student Discipline Procedures (NCSU REG 11.35.02).

Posting any course material to websites like Chegg, ChatGPT, and Course Hero is a violation of copyright law and course policy and is strictly prohibited. Violations of this policy will be reported to the Office of Student Conduct.

Disability Resources

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with the Disability Resource Office at Holmes Hall, Suite 304, 2751 Cates Avenue, Campus Box 7509, 919-515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (NCSU REG 02.20.01).

Students who receive accommodations are responsible for filing those accommodations officially with DRO before the tests occur. It is not appropriate to tell the instructor that you should receive accommodations without going through the official channels. The instructor will only adjust test conditions after receiving the official Accommodation Letter Notification from DRO. Adjustments are never made retroactively to past examinations.

Digital Course Components

Because of the way our course is structured, students need internet connectivity in order to read course materials and complete assignments. NC State's Office of Information Technology (OIT) provides technology guidance, including requirements and recommendations for computer hardware.

For access to computing hardware, please see the NC State University Libraries Technology Lending and the general Library Computing resources. There are several computers available for use around campus, including in the Mathematics Tutoring Center.

Digitally hosted course components will include but are not limited to Moodle and Zoom.

Software

There are several resources available to assist students with technical or computer issues. For technology help, please consult the Office of Information Technology at NC State University.

Here are some of the primary applications commonly used in online mathematics courses:

You must address the accessibility of these websites for yourself during the course drop/add period.

The instructor is not responsible for ensuring privacy or accessibility of electronic materials that are not required components of the course (e.g., links to supplemental information that is not part of the required reading list). However, the instructor will judiciously consider the privacy, copyright, and accessibility of supplemental links provided to students and warn them of any known issues or concerns in this regard. See Online Course Material Host Requirements (NCSU REG 08.00.11).

Electronically Hosted Components

Please be advised that live meetings for this course may be recorded for current and potential future educational purposes. By your continued participation in this recorded course, you are providing your permission to be recorded. If you would like for your likeness to be edited out of a recorded video, please contact me and I will edit the video accordingly.

Required Statement

Students may be required to disclose personally identifiable information to other students in the course, via digital tools, such as email or web-postings, where relevant to the course. Examples include online discussions of class topics, and posting of student coursework. All students are expected to respect the privacy of each other by not sharing or using such information outside the course.

Additional NC State Rules and Regulations

Your rights and responsibilities

Students are responsible for reviewing the NC State University Policies, Rules, and Regulations (PRRs), which pertain to their course rights and responsibilities, including, but not limited to:

You may also find additional references at NC State Office of Equal Opportunity.

Non-Discrimination Policy

NC State University provides equality of opportunity in education and employment for all students and employees. Accordingly, NC State affirms its commitment to maintain a work environment for all employees and an academic environment for all students that is free from all forms of discrimination. Discrimination based on race, color, religion, creed, sex, national origin, age, disability, veteran status, or sexual orientation is a violation of state and federal law and/or NC State University policy and will not be tolerated. Harassment of any person (either in the form of quid pro quo or creation of a hostile environment) based on race, color, religion, creed, sex, national origin, age, disability, veteran status, or sexual orientation also is a violation of state and federal law and/or NC State University policy and will not be tolerated. Retaliation against any person who complains about discrimination is also prohibited. NC State's policies and regulations covering discrimination, harassment, and retaliation may be accessed at

POL 04.25.05 - Equal Opportunity and Nondiscrimination Policy or the Office of Equal Opportunity

Any person who feels that he or she has been the subject of prohibited discrimination, harassment, or retaliation should contact the Office for Equal Opportunity (OEO) at 919-515-3148.

Support

Everyone is encouraged to take care of themselves and their peers. If you need additional support, there are many resources on campus to help you:

  1. Counseling Center
  2. Health Center
  3. Share a Concern
  4. Pack Essentials

Course Evaluations

ClassEval is the end-of-semester survey for students to evaluate instruction of all university classes. The current survey is administered online and includes 12 closed-ended questions and 3 open-ended questions. Deans, department heads, and instructors may add a limited number of their own questions to these 15 common-core questions.

Each semester students' responses are compiled into a ClassEval report for every instructor and class. Instructors use the evaluations to improve instruction and include them in their promotion and tenure dossiers, while department heads use them in annual reviews. The reports are included in instructors' personnel files and are considered confidential.

Online class evaluations will be available for students to complete during the last two weeks of the semester for full semester courses and the last week of shorter sessions. Students will receive an email directing them to a website to complete class evaluations. These become unavailable at 8am on the first day of finals.

Required statement

This course engages diverse scholarly perspectives to develop critical thinking, analysis, and debate and inclusion of a reading does not imply endorsement. This statement is required per UNC Policy Manual 400.1.6, adopted 12/19/2025.

Syllabus Modification Statement

Our syllabus represents a flexible agreement. It outlines the topics we will cover and the order we will cover them in. Minor changes in the syllabus can occur if we need to slow down or speed up the pace of instruction.

Per REG 02.20.07 – Course Syllabus, syllabi do not constitute an express or implied contract among the student, faculty, or institution. Rather, syllabi serve as a guide for the course.