Required Text
- Calculus - Concepts and Contexts: 4th edition by James Stewart
Supplementary Texts (recommended, and in order of increasing difficulty/abstraction)
- MacLane, Mathematics: Form and Function
Required Text
Supplementary Texts (recommended, and in order of increasing difficulty/abstraction)
Prerequisites: Two years of high school algebra, one year of geometry, and one-half year of trigonometry; or MATH 1150: Precalculus; or placement through the CU Mathematics Placement exam.
Grading: Your grade will be computed as follows:
The two midterms will take place during scheduled class time, from 6 to 7pm on Thursday, October 1 and Thursday, November 5, respectively. The final exam will take place from 6-8pm on Thursday, December 3.
No Makeups: No makeup exams, quizzes, activities or homework will be allowed, without proper documentation. Let's make this class run smoothly, because there is a lot to cover and timeliness is of the essence! The official policy is the following: If you know that you are going to miss an exam or cannot take the final exam at the scheduled time, please notify your instructor at least two classes in advance. If you miss a midterm exam for any acceptable reason (e.g. religious obligation, documented illness), that midterm exam score will be replaced by an estimated score based on your performance on the other midterm. If you miss both exams for acceptable reasons, your midterm scores will be replaced by estimated scores based on your performance on the final. If you miss the final exam and have not rescheduled it in advance, you will score zero on the final or receive an incomplete in the course, depending on the circumstances. You may not reschedule a final exam after the exam has started. In order to be excused from an exam for medical reasons, you must either produce a note from a doctor, or you must obtain prior permission from the instructor to miss the exam. Self diagnosis and self medication are not acceptable for this purpose.
No Late Submissions: No late homework will be accepted, to help develop regularity of habits, as well as to make everybody's lives more bearable--we are on a tight schedule and promptness will be our salvation! I will drop your two lowest homework score to compensate, and I will also do the same for the quizzes.
Submissions Must be PDFs: All submissions must be formatted into a single pdf prior to upload to Canvas. Use a scanning app on your phone if you don't have a scanner. Scanning apps automatically generate pdfs. This applies to homework, quizzes, in-class activities, and exams.
Acquiring WebAssign: We try hard to find the option that is least expensive for students. If you are taking anyother courses with Cengage textbooks, you need only pay once for your subscription to the onlinehomework system, WebAssign. If you are a returning student to the calculus sequence, either inthe MATH or the APPM calculus sequence, you do not need to repurchase the subscription.The required material for the course is a Cengage subscription, available at the bookstore, ordirectly from the publisher (See Cengage for more info.) The subscription includes:
You may purchase a binder-ready (loose-leaf) copy of the textbook from Cengage for approximately $45 (free shipping), or may purchase a hard copy through any other source they choose. Or, youcan buy the textbook from other vendors, but make sure it includes access to the on line homework (Enhanced WebAssign).
Using WebAssign: WebAssign is an on-line system for doing homework. When you log on, you are given problems that you solve on paper and then enter the answers. These problems aregenerally straightforward or computational, and you can repeat them multiple times until you getthe correct answer. The philosophy behind this is that instantaneous feedback is more effectivethan waiting days for a grade, and that doing a problem over if it’s wrong is better than simplyseeing the right answer. Because problems are graded by a computer, there are occasional technicalissues, but we believe the trade-off is worthwhile. WebAssign can be accessed through the link onthe main course webpage. If you added the course after the Friday preceding the start of classes, or if you have switchedsections, then contact Jeff Taylor at math-help@colorado.edu so he can enroll you in WebAssign.Include your first and last name, your CU email address, your IdentiKey username, and the courseand section number you are enrolled in. You can find your WebAssign Assignments by clicking onthe following link: https://www.webassign.net/colorado/login.html. There is a two-weektrial periodin the beginning of the semester during which all enrolled students may use WebAssign without an access code.There will be a WebAssign assignment for each topic we cover, assigned when we begin that material. Please check the due dates regularly, as you are responsible for getting the assignments done on time. No late WebAssign will be accepted and no extensions will be granted. However, we will allow you to miss 10% of the WebAssign problems for the semester with no penalty, so you don’t need to panic if you miss a problem here and there.
Homework: You will be assigned several conceptual problems each week. These problems are a variety of problems from the textbook, along with supplement problems. You are expected to write up complete, legible, and logical solutions to these problems, which will be graded by your instructor. Each problem should be written using complete sentences to explain your steps. You may work with one or more of your classmates to understand the problems and even to solve them (in fact, we recommend it); however, you must independently write up your solutions in your own words. Thus it is your own language and your own work that you turn in to be graded. If you are wondering if you crossed the line, ask yourself “Could I start over and redo this on my own, and would it basically look like this?” If not, then you are submitting someone else’s work (plagiarism). Copying homework solutions from the internet also constitutes plagiarism. All cases of plagiarized homework will be submitted to the Honor Code Board. Homework will be collected and returned in your Thursday recitation. Late homework will not be accepted, but your lowest two homework scores will be dropped. Your homework must be stapled and labeled with your section number to be counted for credit.
In-Class Activities: At various times in this class you will work on short projects and activities in small groups with several of your classmates. Expect to be assigned to groups, which will be changed frequently. I will be present during recitations to facilitate your work on the projects, but the goal is for you (and your group-mates) to work through, and complete these projects on your own as much as possible. I will be making sure that you participate in your group’s explorations and discoveries. Your grade is partially based on participation, so participate. Missed projects/activities cannot be made up: if you miss class when such projects/activities are held, you will receive a zero for it. However your lowest two project/activity grades will be dropped.
Students With Disabilities: If you qualify for accommodations because of a disability, please submit your accommodation letter from Disability Services to your faculty member in a timely manner (at least one week before the exam) so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities in the academic environment. Information on requesting accommodations is located on the Disability Services website www.colorado.edu/disabilityservices/students. Contact Disability Services at 303-492-8671 or dsinfo@colorado.edu for further assistance. If you have a temporary medical condition or injury, see Temporary Medical Conditions under the Students tab on the Disability Services website and discuss your needs with your professor.
Calculators and Other Technology: You are required to have an electronic device that can access the internet, so a smart phone, laptop, or tablet for in-class activities and online assessments. The device you use should be capable of graphing functions, so you will need a graphing application, including the free app Desmos. Absolutely no such devices will be allowed, or will be needed for, any assessments.
Mathematics Academic Resource Center: The Mathematics Academic Resource Center (MARC) is a free service provided by the Department of Mathematics that offers students additional support for their CU Mathematics courses. In an effort to help curtail the spread of COVID-19,the Department is offering the MARC exclusively online for the fall semester. For the time being,the MARC will be the MARCO (O for Online).
Student Classroom and Course-Related Behavior: Students and faculty each have responsibility for maintaining an appropriate learning environment. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. For more information, see the policies on classroom behavior and the Student Code of Conduct.
Statement on Discrimination and Harassment: The University of Colorado Boulder (CU Boulder) is committed to fostering a positive and welcoming learning, working, and living environment. CU Boulder will not tolerate acts of sexual misconduct intimate partner abuse (including dating or domestic violence), stalking, protected-class discrimination or harassment by members of our community. Individuals who believe they have been subject to misconduct or retaliatory actions for reporting a concern should contact the Office of Institutional Equity and Compliance (OIEC) at 303-492-2127 or cureport@colorado.edu. Information about the OIEC, university policies, anonymous reporting, and the campus resources can be found on the OIEC website.
Honor Code: All students enrolled in a University of Colorado Boulder course are responsible for knowing and adhering to the academic integrity policy. Violations of the policy may include: plagiarism, cheating, fabrication, lying, bribery, threat, unauthorized access to academic materials, clicker fraud, submitting the same or similar work in more than one course without permission from all course instructors involved, and aiding academic dishonesty. Incidents of academic misconduct may be reported to the Honor Code Council (honor@colorado.edu; 303-735-2273). Students who are found responsible for violating the academic integrity policy will be subject to nonacademic sanctions from the Honor Code Council as well as academic sanctions from the faculty member. Additional information regarding the academic integrity policy can be found at the Honor Code Office website.
Requirements for COVID-19: As a matter of public health and safety due to the pandemic, all members of the CU Boulder community and all visitors to campus must follow university, department and building requirements,and public health orders in place to reduce the risk of spreading infectious disease. Required safety measures at CU Boulder relevant to the classroom setting include:
Students who fail to adhere to these requirements will be asked to leave class, and students who do not leave class when asked or who refuse to comply with these requirements will be referred to Student Conduct and Conflict Resolution. For more information, see the policies on COVID-19 Health and Safety and classroom behavior and the Student Code of Conduct. If you require accommodation because a disability prevents you from fulfilling these safety measures, please see the Accommodation for Disabilities statement on this syllabus. Before returning to campus, all students must complete the COVID-19 Student Health and Expectations Course. In this class, if you are sick or quarantined, please let us know that you are unable to attend class in-person and/or remotely, and provide us with an estimate for the duration of your absence.
Preferred Student Names and Pronouns: CU Boulder recognizes that students’ legal information doesn’t always align with how they identify. Students may update their preferred names and pronouns via the student portal; those preferred names and pronouns are listed on instructors’ class rosters. In the absence of such updates, the name that appears on the class roster is the student’s legal name.
Religious Observances: Campus policy regarding religious observances requires that faculty make every effort to dealreasonably and fairly with all students who, because of religious obligations, have conflicts withscheduled exams, assignments or required attendance. See the campus policy regarding religiousobservances for full details.
Sexual Misconduct, Discrimination, Harassment and/or Related Retaliation: The University of Colorado Boulder (CU Boulder) is committed to fostering an inclusive andwelcoming learning, working, and living environment. CU Boulder will not tolerate acts of sexualmisconduct (harassment, exploitation, and assault), intimate partner violence (dating or domesticviolence), stalking, or protected-class discrimination or harassment by members of our community.Individuals who believe they have been subject to misconduct or retaliatory actions for reporting aconcern should contact the Office of Institutional Equity and Compliance (OIEC) at 303-492-2127 orcureport@colorado.edu. Information about the OIEC, university policies, anonymous reporting,and the campus resources can be found on the OIEC website. Please know that faculty and instructors have a responsibility to inform OIEC when madeaware of incidents of sexual misconduct, dating and domestic violence, stalking, discrimination,harassment and/or related retaliation, to ensure that individuals impacted receive informationabout options for reporting and support resources.
Pascal, in the opening lines of his Of the Geometrical Spirit (c 1657) says, `We may have three principal objects in the study of truth: one to discover it when it is sought; another to demonstrate when it is possessed; and a third, to discriminate it from the false when it is examined. I do not speak of the first [this is speculation, or insight, and involves ingenuity and creativity--these are not uniformly distributed among people and so do not constitute a method]; I treat particularly of the second, and it includes the third. For if we know the method of proving the truth, we shall have, at the same time, that of discriminating it, since, in examining whether the proof that is given of it is in conformity with the rules that are understood, we shall know whether it is exactly demonstrated.`
He then proceeds to explain the method of proof. Step one is establishing clear definitions, step two is proofs, `never advancing any proposition which could not be demonstrated by truths already known,` whether those be previously proven propositions, our established definitions or the assumed axioms of the subject.
Pascal elaborates more fully on the proper methods of proof in another essay, The Art of Persuasion: 'This art, which I call the art of persuading, and which, properly speaking, is simply the process of perfect methodical proofs, consists of three essential parts: of defining the terms of which we should avail ourselves by clear definitions; of proposing principles or evident axioms to prove the thing in question; and of always mentally substituting in the demonstrations the definition in the place of the thing defined.'
'The reason of this method is evident,' says Pascal, 'since it would be useless to propose what it is sought to prove, and to undertake the demonstration of it, if all the terms which are not intelligible had not first been clearly defined; and since it is necessary in the same manner that the demonstration should be preceded by the demand for the evident principles that are necessary to it, for if we do not secure the foundation we cannot secure the edifice; and since, in fine, it is necessary in demonstrating mentally, to substitute the definitions in the place of the things defined, as otherwise there might be an abuse of the different meanings that are encountered in the terms. It is easy to see that, by observing this method, we are sure of convincing, since the terms all being understood, and perfectly exempt from ambiguity by the definitions, and the principles being granted, if in the demonstration we always mentally substitute the definitions for the things defined, the invincible force of the conclusions cannot fail of having its whole effect.'
Significant portions of these two essays are devoted to discussing key nuances of the method, which require skill, even art, to master:
Two special topics round out his discussion, both in Of the Geometrical Spirit.
The stage has been set for the development of calculus, whose full logical articulation is analysis.
Research shows that people learn mathematics best when they are actively participating. In other words, you learn by doing, not by watching. Therefore, MATH 1300 does not meet in large sections, but instead meets in small sections, which allows individual and group work in which you will be actively engaged, solving problems, making discoveries and understanding connections. This course and the book we are using are designed for a classroom which does not follow a traditional lecture format. Do not be surprised if your instructor often spends only half a class period lecturing or solving problems; the rest of the time, you should expect to be working at your desk or remotely, either individually or in groups, presenting your work.
In this vein, you will be expected to read a section in the book before it is discussed in class. Lectures are intended to highlight aspects of the text, not to replace it. In this course you will learn a number of useful formulas, though their mastery is not the primary purpose of calculus any more than correct spelling is the primary purpose of literature. Our goal is to have you learn how to understand calculus conceptually so you can build your own approaches to solving practical problems. We will use a variety of in-class activities where you will collaborate in small groups to discover, extend, and apply calculus concepts.
About Calculus: Roughly speaking, calculus is the mathematics of change. In particular, calculus is a powerful tool for understanding change in physical quantities and phenomena that depend on, or are related to, each other. The dependence of a given quantity upon another (or others) is often described mathematically by a function. Thus, the heart of calculus is the study of functions, andhow they change. Differential calculus studies the instantaneous change of a function as quantities vary, and integral calculus measures the cumulative effect of the change of a function. Calculus has led to profound human achievements: initially created to solve basic geometric problems, it soon led to a nearly complete understanding of the motion of the planets. Nowadays calculus is applied constantly in mathematics, chemistry, economics, biology, psychology, physics, and every type of engineering. However, it need not be viewed only as a tool: it arose from human imagination and is capable of creating great beauty on its own.
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