Counterexamples in calculus mathematical association of america. Students must find the value of hyperbolic functions and also find derivatives and integrals. The following major topics from a typical course on calculus of a single variable are considered. A big proportion of students seem to be able to find correct solutions to test and. Counterexamples in calculus classroom resource materials. Shorser this proof structure allows us to prove that a property is not true by providing an example where it does not hold. Logic correspondingly treats inferences in terms of collections of statements, which are called. Check your understanding of counterexamples in math in this quiz and worksheet. Create the worksheets you need with infinite calculus.
Obtaining counterexamples is a very important part of mathematics, because doing mathematics requires that you develop a critical attitude toward claims. Even for such a small book, addressing these issues might help the inexpert intended audience. Counterexamples in calculus unfortunately does not contain a glossary, nor an index, and there are a few trivial proofing errors. This video gives 4 example problems explaining counterexamples to conditional statements. Quickly find the exact topics you need and print out worksheets for your students to practice the. Erdman portland state university version august 1, 20 c 2010 john m. Some of the incorrect statements are converses of wellknowntheorems.
This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool. This site is like a library, use search box in the widget to get ebook that you want. However, i found the book thoughtprovoking, even fun, and i heartily recommend it to you and your students. The first 2 examples are the basics behind counterexamples. Counterexamples in calculus is a resource for singlevariable calculus courses. They are excellent problems in preparation for examinations. David jones revised the material for the fall 1997 semesters of math 1am and 1aw.
In some cases, such as lhospitals rule, this is simply an introduction to a concept. If a number is greater than 3, then the number is greater than 5. Counterexamples are often used in math to prove the boundaries of possible theorems. Counterexamples in teachinglearning of calculus core.
Further, counterexamples very often add to students intuition and ability to quickly recognize false propositions. V o ra ol fl 6 6r di9g 9hwtks9 hrne7sherr av ceqd1. Click download or read online button to get counterexamples in calculus book now. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples. Lectures on counterexamples in several complex variables. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. Students will identity geometric and numerical patterns. Counterexamples in calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. Basic concepts 3 treats all of these things in terms of a single sort of thing statements. Accompanying the pdf file of this book is a set of mathematica notebook files. Conjectures and counterexamples problems are also given. Counterexamples a counterexample is an example that disproves a universal for all statement. The files are available in portable document format pdf or in postscript ps.
Be prepared to justify your answer with an argument or counterexample. This free calculus worksheet contains problems on hyperbolic functions. Constructions, characterizations and counterexamples. Incorrect statements are grouped topically with sections devoted to functions, limits, continuity, differential calculus and integral calculus. Below students will find blank worksheets they may print when absent or when they have misplaced their original copy. Christine heitsch, david kohel, and julie mitchell wrote worksheets used for math 1am and 1aw during the fall 1996 semester. Functions, limits, continuity, differential calculus and integral. This twopage activity guides students to practice writing conditional statements, converses, and biconditionals about animals and triangles. A counterexample is a special kind of example that disproves a statement or proposition. They apply the rules of limits to solve functions where the limit of x. This booklet contains the worksheets for math 1a, u. High school teaching resources education jobs, teaching. Apply the power rule of derivative to solve these pdf worksheets.
Find the counterexample to the following conditional statement. On the first page, they are given diagrams with one piece of information either. Methods of producing these incorrect statements vary. This serves to illuminate some of the key reasons and major technical obstacles for the extensive recent development of analytic. When you have an idea or when someone tells you something, test the idea by trying examples. Mathematical logic exercises chiara ghidini and luciano sera.
Pdf on jan 1, 2010, sergiy klymchuk and others published counterexamples in calculus find, read and cite all the. Counterexamples in calculus download ebook pdf, epub. In this calculus worksheet, students evaluate functions and solve problems using the derivative. Functions, limits, continuity, differential calculus and i ntegral calculus. Line number 18088 abbreviated syllabus for full details, a daytoday schedule including assignments, handouts. Understanding basic calculus graduate school of mathematics. Counterexamples in caculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses.
This booklet contains worksheets for the math 180 calculus 1 course at the university. Give a counterexample that disproves each conjecture below. Surprises and counterexamples in real function theory. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. This worksheet contains introductory questions on conditional statements and converses. Geometry building blocks solutions, examples, worksheets. Conditional statements, converses, counterexamples, truth.
Geometry name worksheet counterexamples date period. Use these practice questions to see what you know before watching. Math 129 calculus ii worksheets the following is a list of worksheets and other materials related to math 129 at the ua. Counterexamples and negations of conditional statements the real number \x 1\ in the previous example was used to show that the statement \\forall x \in \mathbbr x3 \ge x2\ is false. Calculus without tears ctw is a collection of worksheets in 3 volumes that teaches the basic concepts of calculus very stepbystep, without a need of much algebra. Math 122b first semester calculus and 125 calculus i worksheets the following is a list of worksheets and other materials related to math 122b and 125 at.
Math 180 calculus 1 worksheets university of illinois at chicago. The material was further updated by zeph grunschlag. H t2 x0h1j3e ik mugtuao 1s roafztqw hazrpey tl klic j. This book provides a onesemester undergraduate introduction to counterexamples in calculus and analysis. The counterexamples presented here are the first of this kind for notions of differentiability that satisfy a chain rule. Counterexamples in calculus mathematical association of. For example, to prove that \not all triangles are obtuse, we give the following counter example. Pdf this book makes accessible to calculus students in high school, college and university a range of counterexamples to conjectures that.
Counterexamples show why the hypotheses of various theorems are important. Exercises in calculus by norman dobson, edited by thomas gideon forward these exercises were given by the late norman dobson under the title final exam problems. Patterns and inductive reasoning this is a good worksheet for early in a new year of geometry. Their context arises naturally from requiring differentiability of crucial maps in the theory of pseudoholomorphic curves in symplectic geometry. We have english resources for all years, math resources and worksheets or world language resources and flashcards. Derivative worksheets include practice handouts based on power rule, product rule, quotient rule, exponents, logarithms, trigonometric angles, hyperbolic functions, implicit differentiation and more. Our 11th grade math worksheets cover topics taught in algebra 2, trigonometry, and precalculus. Some examples of counterexamples that could be provided in a first year calculus course include.