Math 1051 Precalculus I Syllabus for Fall 2016 Course: Math 1051 is a School of Mathematics course that is the first in a two-course sequence that covers the content of a standard precalculus course. We begin with a quick review of high school algebra and then move on to examine the behavior of functions in some depth including inverses, transformations, and compositions. We pay particular attention to linear, quadratic, polynomial, rational, exponential, and logarithmic functions and their graphs. There is no trigonometry in Precalculus I. Trig is covered in Math 1151 Precalculus II. For students who wish to move at a faster pace, Precalculus I & II are combined into a single course, Math 1155 Intensive Precalculus. Precalculus II and Intensive Precalculus each prepare students for the calculus sequence while Precalculus I prepares students for Precalculus II and Math 1142 Short Calculus. Lecturer: Professor Robertson, 270D Peik Hall, (in the Knoll Area between the river and University Avenue), [email protected], 612-625-1075. Postal Mail: 125 Peik Hall, 159 Pillsbury Drive SE, Minneapolis, MN 55455-0208 Campus Mail: 125 Peik Hall (delivery code 4301) I am a visiting professor from the Department of Curriculum and Instruction (CI), which is in the College of Education and Human Development. You can see my bio on my web site (see below). My office hours are Tue and Thu 10 am to 11 am. If you would like to see me at other times call or email and we can set up something. Web Site: My web site has information relevant this course such as handouts, practice exams, exam keys, this syllabus, my lecture notes, and the schedule of assignments. It also has information on other courses I teach, including CI 0832 Algebra Review, which is the prerequisite for Math 1051. My web site URL is http://z.umn.edu/robertson Course Prerequisites: To have a reasonable chance of being successful in this course you should have completed at least three years of high school mathematics, or CI 0832 here at the U, with a grade of at least C and you still remember the material! Information on the kinds of things you should know before taking Math 1051 can be found in the document Why Math Placement on my web site. If you have any questions about your placement in Precalculus talk to me. LEC section 10 meets with Professor Robertson MWF 10:10 AM to 11:00 AM in 275 Nicholson Hall. Discussion (DIS) sessions meet on Tuesdays and Peer Assisted Learning (PAL) sessions meet on Thursdays at various times and locations. If you need to get into a closed section or want to switch sections send an email to [email protected]telling them what you want to do and giving them your name, U of M ID number, and your college. Cell Phones: Please turn off your cell phone before entering class. You may NOT use a cell phone, tablet, or graphing calculator during exams. Course Materials: The following are available at Coffman Bookstore. The current hours for the bookstore are available at http://www.bookstore.umn.edu or by calling 612-625-6000. • Textbook: Precalculus, ninth edition, by Michael Sullivan, Prentice Hall, 2012. There are several "versions" of the book. The bookstore has stocked Custom Edition Volume I (ISBN: 9781269957847). This contains the Appendix and Chapters 1 through 5. A Student Solutions Manual (SSM) that contains the solutions to the odd-numbered homework problems may also be available at the bookstore or at Amazon.com. Or, in the past we used a softcover custom book that, in addition to Chapters 1 through 5, contained Chapters 6 through 12. So, if you find a cheap used custom edition that has all twelve chapters that is fine to use this semester. Or, you can use the standard hardcover 9 th edition (available at Amazon and elsewhere, but probably more expensive).
Transcript
Math 1051 Precalculus I Syllabus for Fall 2016
Course: Math 1051 is a School of Mathematics course that is the first in a two-course sequence that covers the content of a standard precalculus course. We begin with a quick review of high school algebra and then move on to examine the behavior of functions in some depth including inverses, transformations, and compositions. We pay particular attention to linear, quadratic, polynomial, rational, exponential, and logarithmic functions and their graphs. There is no trigonometry in Precalculus I. Trig is covered in Math 1151 Precalculus II. For students who wish to move at a faster pace, Precalculus I & II are combined into a single course, Math 1155 Intensive Precalculus. Precalculus II and Intensive Precalculus each prepare students for the calculus sequence while Precalculus I prepares students for Precalculus II and Math 1142 Short Calculus.
Lecturer: Professor Robertson, 270D Peik Hall, (in the Knoll Area between the river and University Avenue), [email protected], 612-625-1075.
Postal Mail: 125 Peik Hall, 159 Pillsbury Drive SE, Minneapolis, MN 55455-0208 Campus Mail: 125 Peik Hall (delivery code 4301)
I am a visiting professor from the Department of Curriculum and Instruction (CI), which is in the College of Education and Human Development. You can see my bio on my web site (see below).
My office hours are Tue and Thu 10 am to 11 am. If you would like to see me at other times call or email and we can set up something.
Web Site: My web site has information relevant this course such as handouts, practice exams, exam keys, this syllabus, my lecture notes, and the schedule of assignments. It also has information on other courses I teach, including CI 0832 Algebra Review, which is the prerequisite for Math 1051. My web site URL is http://z.umn.edu/robertson
Course Prerequisites: To have a reasonable chance of being successful in this course you should have completed at least three years of high school mathematics, or CI 0832 here at the U, with a grade of at least C and you still remember the material! Information on the kinds of things you should know before taking Math 1051 can be found in the document Why Math Placement on my web site. If you have any questions about your placement in Precalculus talk to me.
LEC section 10 meets with Professor Robertson MWF 10:10 AM to 11:00 AM in 275 Nicholson Hall. Discussion (DIS) sessions meet on Tuesdays and Peer Assisted Learning (PAL) sessions meet on Thursdays at various times and locations. If you need to get into a closed section or want to switch sections send an email to [email protected] telling them what you want to do and giving them your name, U of M ID number, and your college.
Cell Phones: Please turn off your cell phone before entering class. You may NOT use a cell phone, tablet, or graphing calculator during exams.
Course Materials: The following are available at Coffman Bookstore. The current hours for the bookstore are available at http://www.bookstore.umn.edu or by calling 612-625-6000.
• Textbook: Precalculus, ninth edition, by Michael Sullivan, Prentice Hall, 2012. There are several "versions" of the book. The bookstore has stocked Custom Edition Volume I (ISBN: 9781269957847). This contains the Appendix and Chapters 1 through 5. A Student Solutions Manual (SSM) that contains the solutions to the odd-numbered homework problems may also be available at the bookstore or at Amazon.com.
Or, in the past we used a softcover custom book that, in addition to Chapters 1 through 5, contained Chapters 6 through 12. So, if you find a cheap used custom edition that has all twelve chapters that is fine to use this semester.
Or, you can use the standard hardcover 9th edition (available at Amazon and elsewhere, but probably more expensive).
Page 2 Math 1051 Lecture Section 10 Syllabus for Fall 2016
• Calculator: A $15 scientific calculator is sufficient for this course. You may not use a cell phone, tablet, or graphing calculator, or one that does symbolic manipulation, when taking an exam, but you can use those while doing homework.
• Miscellaneous supplies including pens, pencils, pencil sharpener, stapler, staples, scissors, spiral notebooks (for taking notes in class), loose-leaf paper (for doing assignments to be handed in), a packet of graph paper (for sketching x-y graphs—for printable graph paper see http://www.z.umn.edu/robertson), file folders (for organizing your papers), an accordion folder (to hold the file folders), and a calendar to keep track of homework, quiz, and exam dates. Being organized right from the start will help you use your time more efficiently.
Mathematical Thinking Requirement: Math 1051 meets the Mathematical Thinking Diversified Core portion of the Liberal Education requirements of the University of Minnesota. All students must meet this requirement before they can graduate from the U, no matter what their major.
What is Liberal Education? A college education is not a job training program so, for example, if you want to learn refrigeration repair then you should attend a technical school or join the military. A liberal education is, "an education conducted in a spirit of free inquiry undertaken without concern for topical relevance or vocational utility. This kind of learning is not only one of the enrichments of existence, it is one of the achievements of civilization. It heightens students' awareness of the human and natural worlds they inhabit. It makes them more reflective about their beliefs and choices, more self-conscious and critical of their presuppositions and motivations, more creative in their problem-solving, more perceptive of the world around them, and more able to inform themselves about the issues that arise in their lives, personally, professionally, and socially. College is an opportunity to learn and reflect in an environment free from most of the constraints on time and energy that operate in the rest of life.
"A liberal education is also a preparation for the rest of life. The subjects that undergraduates study and, as importantly, the skills and habits of mind they acquire in the process, shape the lives they will lead after they leave the academy. Some of our students will go on to become academics; many will become physicians, lawyers, and businesspeople. All of them will be citizens, whether of the United States or another country, and as such will be helping to make decisions that may affect the lives of others. All of them will engage with forces of change — cultural, religious, political, demographic, technological, planetary. All of them will have to assess empirical claims, interpret cultural expressions, and confront ethical dilemmas in their personal and professional lives. A liberal education gives students the tools to face these challenges in an informed and thoughtful way."1
You are required to take a mathematics course because an important component of a liberal education is an appreciation of mathematics as a body of thought which has been developed over the millennia for aesthetic reasons, to address the natural curiosity of humans concerning the world in which we live, and to solve problems. You will learn how mathematicians think and view the world through my lectures and your group work, discussions, homework, and reading the textbook. You will become familiar with the “ways of knowing” of mathematicians.
Math 1051 addresses the value of a Liberal Education by immersing you in a mathematically-based exploration of the creativity of the human mind. For example, we will examine the seemingly
1 Adapted from “The Value of a Liberal Arts Education”, http//www.admissions.college.harvard.edu/about/learning/liberal_arts.html
Math 1051 Lecture Section 10 Syllabus for Fall 2016 Page 3
impossibility of infinity and how it can be used; we will look at the nature of Euler’s number2 from a theoretical perspective and then see how it “pops up” in places like calculating compound interest, measuring the cooling of a substance, and describing the spread of an infectious disease. You will experience the relevance and value of mathematics as a part of a liberal education that promotes critical and creative thinking, aesthetic appreciation, and the contributions that many cultures have made to the development of mathematics. You will develop an ability to better understand the human mind and the human condition through a mathematical lens.
In this course we will look at the nature of mathematics as a science, a way of thinking, and an art form whose elegance rivals the works of Italian painter, sculptor, architect, scientist, musician, mathematician Leonardo da Vinci (1452-1519), Spanish painter Pablo Picasso (1881-1973), and American painter William Henry Johnson (1901-1970).
Leonardo da Vinci (1452 - 1519) Pablo Picasso (1881 - 1973) William Henry Johnson (1901-1970)
Like spoken languages, mathematics provides a way of communicating thoughts and ideas, but it does so in a formal and logical way. One of the powerful aspects of mathematics is that people of all cultures and backgrounds can agree on the logic of what it has to say and how it says it. In his book Is God a Mathematician, Mario Livio notes that there is “overwhelming evidence of a universe that is either governed by mathematics or, at the very least, susceptible to analysis through mathematics.” Of course, at the frontiers of mathematics, people still argue and disagree as they always have but usually, eventually, the evidence and logic and truth of mathematical ideas prevail and become universally accepted, or they are thrown out if they are proven to be false or inconsistent with that which we know to be true or with what we have defined.
At the heart of much of modern mathematics is the algebra of equations and functions. The first symbolic approach to equations began in the Arab world during the 9th century AD, and the concept of function was first introduced in the 14th century. But it was the advent of calculus that made the algebra of equations and functions central to so many applications of mathematics. That is why Math 1051 focuses on using algebra to solve equations and analyze some basic families of functions. It will help prepare you for the kind of mathematical thinking that is central to calculus, and hence to much of modern mathematics.
Math 1051 covers topics in algebra that are of intrinsic mathematical interest, have important applications, and which are needed for a full understanding of calculus. Your work in this course will help to develop in you an understanding of the symbolic language of mathematics and will give you ample opportunity to experience how mathematics is done by mathematicians, scientists, engineers, economists, psychologists, etc. as you solve problems, communicate your results, and learn how abstract mathematical concepts can be applied to the real world.
2 Euler’s number was discovered by Jacob Bernoulli around 1685. It was given the symbol e by Leonhard Euler in 1736.
Here are two ways of defining it
1lim 1 2.718281828459...
n
ne
n and
0
1 1 1 11 ...
! 1 1 2 1 2 3
n
en
Page 4 Math 1051 Lecture Section 10 Syllabus for Fall 2016
A key concept developed in this course is the idea of modeling. A model is a representation of something. For example, a model airplane is a replica of a real airplane. Models come in many
types, shapes, sizes, and levels of complexity. For example, you can make a simple model of a Boeing 787 Dreamliner by folding paper in a certain way. It is quick, easy, and cheap but only very roughly approximates the real thing. Depending on your purposes, that model might be all you need. If you need a more precise model, one that you will use in a wind tunnel to research the aerodynamics of a 787, you will need something more detailed, complex, and expensive.
We can model both real-world phenomenon (e.g., how demand and supply of a product are related to price and quantity produced and bought) or we can model make-believe phenomenon (e.g., how an avatar will behave in various situations).
This class will introduce you to mathematical modeling, which entails constructing mathematical representations of situations, things, or processes. To construct our mathematical models we will use both Theoretical Modeling and Empirical Modeling.
In Theoretical Modeling, we use mathematics and theories from such diverse fields as physics and economics to construct a representation of a situation, a thing, or a process. We develop the model from a rich base of knowledge, building on what others have learned before us. For example, we will examine the mathematics of using radioactive decay of Carbon-14 to determine the age of ancient dwellings.
In Empirical Modeling, we gather data from a particular situation and then use mathematics to discover patterns and relationships that describe the data as best we can. For example, we will use automobile performance data to determine the speed at which a particular type of automobile achieves its best fuel efficiency.
In both types of modeling you will develop expressions, equations, and quantitative ideas that represent the behavior of some phenomena.
The mathematics we develop can be used to make predictions about phenomena that have not yet occurred (e.g., What will the Stock Market do tomorrow if the Federal Reserve3 lowers interest rates by 1/2 percent today?). As you learn and do more and more mathematics you will cultivate a feel for how people develop, select, and fine-tune mathematical models to represent a wide variety of situations. Such knowledge is essential for you to be an informed citizen and a liberally educated person who is able to understand and make decisions in the real world.
Why study mathematics? Here are a few good reasons from historical figures:
In 500 BC the Pythagorean Brotherhood said the study of mathematics aided spiritual development.
In 1800 John Arbuthnot wrote that mathematics “charms the passions, restrains the impetuosity of the imagination, and purges the mind of error and prejudice.”
In 1906 J. C. Fitch noted that studying mathematics which you will never have a need for “helps one to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.”
In 1942 the Navy found that officers who had completed a course in calculus were better officers than those who had not.
In 1984 Underwood Dudley noted that mathematics is so beautiful that “some theorems and their proofs, those which cause us to gasp or to laugh out loud with delight, should be hanging in museums.”
3 The Federal Reserve is the central banking system of the United States.
Math 1051 Lecture Section 10 Syllabus for Fall 2016 Page 5
Course Goals The primary goals of this course are to expand your mathematical knowledge base and to help you to develop a “feel” for what mathematics is and what mathematicians do. Specific goals include
• Understand and appreciate that mathematicians have made a difference to humankind, both in their time and in the current world. Without their efforts and hard work to develop mathematics and its applications, our world today would be very different. Mathematics is all around us, from the Cartesian coordinate system of Frenchman Rene Descartes (1596-1650) that allows us to see mathematical functions as pictures, to the calculus of Englishman Isaac Newton (1643-1727) and German Gottfried Leibniz (1646-1716), which allows us to build the machines, bridges, and buildings we use daily, to the counting theories of American Ronald Graham (1935-present) used to develop schedules for NASA, railroads, highways, and air traffic, to the theories of stellar formation and evolution of astrophysicist Neil deGrasse Tyson (1958-present) which help us to understand the structure of the Universe. Without the giants of mathematics on whose shoulders others stand, we would live in a much more primitive society.
Descartes 1596-1650 Newton 1643-1727 Leibniz 1646-1716 Graham 1935- deGrasse Tyson 1958-
• Understand the analytic and graphical behaviors of linear, quadratic, polynomial, rational, exponential, and logarithmic functions.
• Master algebraic methods of simplifying expressions and solving equations based on these functions.
• Use mathematical models to make predictions about real-world situations.
• Develop an ability to look at mathematics from several perspectives including4
Mathematical problem solving—using problem solving strategies, formulating problems, and applying mathematical modeling to real-world applications.
Mathematical communication—using language to communicate mathematical ideas in writing, clarifying thinking, formulating definitions, expressing generalizations, reading mathematics with understanding, asking proper questions, and employing mathematical notation.
Mathematical reasoning—making and testing conjectures, formulating counter examples, constructing and evaluating valid arguments.
Mathematical connections—recognizing equivalent representations and using mathematics in applications.
4 From Cohen, D. Crossroads in Mathematics Standards for Introductory College Mathematics before Calculus. Memphis American Mathematical Association of Two-Year Colleges, 1995.
Page 6 Math 1051 Lecture Section 10 Syllabus for Fall 2016
Student Learning Outcomes (SLOs) Math 1051 addresses the following SLOs as outlined at http//academic.umn.edu/provost/teaching/cesl_loutcomes.html
1. Identify, define, and solve problems You will gain experience identifying, defining, and solving problems by creating mathematical models that will help you make predictions to see how a situation will evolve in time (e.g., find the future value of an investment).
3. Master a body of knowledge and a mode of inquiry You will increase your mathematical knowledge base, especially in the area of functions, and you will do a lot of the symbolic manipulation typically found in a first college mathematics course.
5. Communicate effectively Mathematics is a language with a precise vocabulary and syntax. Knowledge of these is necessary in order for you to effectively communicate your findings to others so they can be enriched by the knowledge and so they can use what you have discovered for real world problem solving. Communicating mathematically is not just getting "the right answer;" it involves showing how the answer was arrived at and helping your audience comprehend and agree with your conclusions. In fact, on our in-class tests, getting the correct answer to a problem will not be sufficient; you will have to show, convincingly, how you arrived at that answer using proper mathematics.
6. Understand the role of creativity, innovation, discovery, and expression across disciplines Mathematics is a human endeavor, sometimes developed to solve practical problems and other times written like a Shakespearian poem to express ideas, conjectures,
patterns, and facts in a beautiful and graceful form, such as Euler’s Identity 1 0ie , which is considered by many to be the most elegant equation ever discovered or created.
Some people think that mathematics is a fundamental feature of the universe and that humans are "discovering" what is already there. Others think humans are creating mathematics through innovative thought and hard work. As we look at some of the historical developments in mathematics you will have to decide for yourself which it is. In either case you should come to realize and appreciate the role of creativity, innovation, and discovery that mathematics has engendered throughout the ages and across cultures.
7. Effective citizenship and life-long learning The skills, concepts, and knowledge you acquire in this course will help you to be an effective citizen in that you will be better able to understand how yourself and others can use mathematics to help make decisions and predictions.
For example, when meteorologists talk about computer models predicting the path of a hurricane you will have a feeling for what a model is, how it is developed, and how different assumptions used in the development stages of alternative models can lead to different predictions (e.g., one hurricane model may predict the storm will turn south into Mexico while another model may predict it will turn north into New Orleans). This is a lesson in how intelligent and honest people can analyze the same data and come to different, perhaps even contradictory, conclusions.
Course Structure Math 1051 class meetings consist of three parts:
MWF Lectures: The primary source of new material in this course will be the textbook and the Monday-Wednesday-Friday large classroom lectures. I will explain the mathematics, provide worked examples, and have you work some problems in class. Attending the lectures is very important—students who skip the lectures tend to fail the course. Your work during lecture will count for 5% of your final grade.
Math 1051 Lecture Section 10 Syllabus for Fall 2016 Page 7
Tuesday Discussion Sessions: Each Tuesday, you will attend a discussion session that is led by a mathematics graduate teaching assistant (GTA). The GTA will do some sample problems that will be similar to those that will appear on the exams and answer any questions you have on the material or the homework. Your GTA will also collect your homework and return your graded homework and exams. Your homework will count for 15% of your final grade.
Thursday PAL Sessions: Each Thursday, you will attend a Peer Assisted Learning (PAL) session. These are small classes where you will work with a PAL facilitator, who is an undergraduate student with a good mathematics background, and your fellow students to actively solve problems using a structured approach. This is not a homework question and answer session but a guided work session designed to help you internalize the processes involved in solving mathematics problems. Your work during PAL sessions will count for 10% of your final grade.
Attendance: You are expected to show up on time for every lecture, discussion, and PAL session and to stay until the class is over. If your schedule or personal habits do not permit this, switch to a section that fits your schedule, take the course through Online and Distance Learning (http://cce.umn.edu/academic-credit-courses), or drop the course. If you can do the work without attending class, you are in the wrong course and you are wasting your time and money; see me or your adviser about switching to a higher level course such as Math 1151 Precalculus II, Math 1155 Intensive Precalculus, or Math 1271 Calculus I.
Expectations: We will provide an environment where you can learn precalculus but, to be successful, you must take an active role within that environment. You will be responsible for learning the material and for getting help when you have questions. While in class you will be expected to make a good faith effort to learn the course material, follow directions, and exhibit behaviors that will improve your chances for success. These behaviors include:
• Showing up for every class on time and prepared.
• Completing all assigned homework on time and with complete worked-out solutions.
• Asking questions when you don't understand something.
• Getting help outside of class from the free tutors (see below).
• Studying and working on mathematics outside of class every day, seven days a week.
Course Difficulty: Although you may have had a course called "Precalculus" in high school, the difficulty, level of abstraction, and expectations generally are much higher at the U. Math 1051 has a 35% non-completion rate (withdrawals and failures) for several reasons:
1. Some students enter the course without a solid knowledge of high school algebra, either because they never learned it well or because they have forgotten large chunks of it. We begin with a three-week review of high school algebra but that goes very fast and is intended as a quick reminder of what you should already know rather than an in-depth treatment of the material. If you think your algebra background is not strong enough to do well in this course talk to me about switching to a lower level course, such as CI 0832 Algebra Review.
2. Many students are not prepared for the large amount of work it will take to learn all the material. It is important for you to memorize many formulas and procedures, but even more importantly you must spend enough time doing mathematics so that you understand the ideas and concepts that form the basis of the formulas and procedures. Understanding what you are doing, and why, takes a commitment that goes far beyond memorizing—we want you to develop a feel for the material in much the same way a pianist develops a feel for her music or an athlete develops a feel for his sport.
Page 8 Math 1051 Lecture Section 10 Syllabus for Fall 2016
3. The course material will get more difficult as the semester progresses. If you start off having difficulties things will only get worse because you must know and understand the beginning material in order to learn the subsequent material. You are taking this course to prepare yourself for calculus which will, in turn, prepare you for higher mathematics, science, and engineering courses. Like any other language, mathematics requires you to build upon your early work as the ideas and concepts become more complicated.
Credits and Workload Expectations: At the U, each class hour is designed to correspond to an average of 3 hours of learning effort per week necessary for an average student to achieve a C in the course. So, an average student shooting for a C (which is way too low a goal for a serious student) taking Precalculus I, which meets 5 hours per week, should expect to spend an additional 10 hours per week on coursework outside the classroom. If mathematics is a difficult subject for you or if you want to get a grade higher than a C then you will have to spend more hours on it. Knowing the material in this course will be crucial to your success in Precalculus II and Calculus. The time you spend on this course will have a great payoff later on.
Time Management: You will need to figure out how to manage the time you spend on this course along with the time you spend on other courses, clubs, athletics, work, social life, travel time, eating, sleeping, etc. Try to make a schedule where you will do things related to this course every day and stick to it. Here are seven quick tips:
1. Be Organized – Make folders for everything and keep them up to date. Save all homework and exams until you see your final grade on your transcript.
2. Plan Ahead – Don’t wait until the last minute to study for exams and quizzes or to do homework.
3. Prioritize Your Tasks – School has to be at least number two, right after sleep.
4. Avoid Overload – Do not overschedule yourself. Learn to say NO! and mean it.
5. Practice Effective Study Techniques – Study in a quiet place where you will not be disturbed and work on math every day. Don’t multi-task or listen to music while doing homework.
6. Be Flexible – Stuff happens so learn to adjust.
7. Have a Vision – Keep reminding yourself why you are enrolled at a world-class research university. Your top objectives should be to learn how to learn, to find out about the world and about yourself. Be curious and question everything. While doing that you also will be acquiring the knowledge, skills, and habits that will make you highly employable. Over an adult's working life there is an average $830,000 income difference between having a college education over just a high school diploma5. So, you actually are getting paid about $16,250 to take this course. Here is the math:
Math 1051 Lecture Section 10 Syllabus for Fall 2016 Page 9
Here is how a typical student might spend his or her time for this class:
Minutes/Wk Task
300 In lecture for 60 minutes 3 days a week. Get there early so you can do the daily warmup problem before lecture begins. Plus 60 minutes for DIS and 60 for PAL.
360 Doing homework, 1 hour per day 6 days per week (7 days would be better).
90 Studying 30 minutes per day 3 days per week after lecture. Go over your notes.
15 Moodle Quizzes, about 3 per week at 5 minutes each. See page 11 of this syllabus.
60 Read the book and also perhaps read my lecture notes on my web site.
80 Study for 4 midterms and the final, about 240 minutes times 5 exams divided by 15 weeks averages to 80 minutes per week (but not evenly spaced).
That comes out to about 15 hours per week. If you struggle with math it will be a lot more; if you are a math wiz, somewhat less.
Earning Extra Credit: There are no opportunities for earning extra credit. Your grade will be based solely on your scores on classwork, homework, quizzes, and exams.
Resources to Help you Learn: You have chosen to attend a world class research university and that means expectations of you are quite high. We will provide you with the resources and environment you need to be successful, but it is up to you to work hard and to fully utilize these resources. Here are some things that will help you succeed:
• Attend every class: Show up to every class prepared and on time.
• Participate in class: Be actively engaged while in class and studying at home. If you don’t become involved in what you are doing you will not learn it very well. Concentrate on what we are doing in class. If you get bored, concentrate even harder!
• Use the textbook: I will not read the textbook to you. For each topic, I will assume that you have read the textbook before the lecture. I will highlight important points and do examples that illustrate the concepts and procedures. If you don’t understand something from the lecture go back to the textbook to get extra instruction and clarification. The textbook is well written but you still will have to read some sections several times before you fully understand them.
• Get help from free mathematics tutors: Free tutors are available through the SMART Learning Commons Free tutors are available through the SMART Learning Commons. To see their current hours of operation and to sign up to work with a tutor, check out their web site at https://www.lib.umn.edu/smart They have drop-in hours at three campus locations: 204 Walter Library on the East Bank, basement of Wilson Library on the West Bank, ground floor Magrath Library on the St. Paul campus.
Page 10 Math 1051 Lecture Section 10 Syllabus for Fall 2016
• Free tutors are available through the Multicultural Center for Academic Excellence. MCAE has an instructional center in 141 Appleby Hall. The Center is a place where students can take their time to learn and where students are not afraid to ask questions. For tutoring schedules go to http://www.mcae.umn.edu/acadsupport/index.html
• Hire your own private mathematics tutor: The School of Mathematics has information on hiring mathematics tutors. For a list of available tutors, send an email to [email protected]
• Get help from your instructors: If you have questions, ask us before, during, or after class or come to our office hours for extra help.
• For a list of available computer help, see http://it.umn.edu/help You can get face-to-face help setting up a computer, getting rid of viruses, connecting to wireless networks, and some repairs at the Tech Stop 101 Coffman Union. Check their web site for their current hours of operation. You can also schedule an appointment online to meet with a technician. Most services are free but some are for a fee. Contact them at 612-301-4357 or [email protected]
• If you would like to get some help in areas such as how to read more efficiently, how to study better for tests, or how to manage time more effectively check out the University Counseling and Consulting Services at http://www.uccs.umn.edu/academic.htm
• Get help from your adviser: Your adviser is there to help you in any way he or she can. Ask your adviser any questions you have on scheduling, requirements, child care, etc.
• Get help from the Student Conflict Resolution Center This center works with students to resolve campus-based problems and concerns. The services are free and confidential. http://www.sos.umn.edu/
Homework Problems: Practicing the skills you learn in this course is of utmost importance. In order to be able to use mathematics you must become automatic at doing symbolic manipulation, such as simplifying expressions, solving equations, and working with functions. Like learning to dance, to play the piano, or to read, learning mathematics involves lots of memorization of what people before you have discovered and then you practicing it until it becomes second nature to you. As the problems become more difficult you will have to perform basic operations and manipulations without thinking about them—they must be automatic. Homework is designed to get you to practice the skills and to help you figure out what you need to spend more time on.
Homework is assigned according to the schedule at the end of this syllabus. Be sure to do every assigned problem; be sure to check the answer of every problem in the back of your textbook or Student Solutions Manual; be sure to do more than the assigned problems if you are having difficulty with a particular topic. Doing mathematics is the only way you can learn it.
Homework ID Numbers: I sent you an email that contains your four-digit homework ID number (HWID). The first two digits are your DIS section number. I use this HWID to keep track of all of your scores so be sure to write your HWID on all homework and exams. If you don’t know your HWID email me at [email protected].
Writing and Turning in Homework Assignments: On lined notebook paper or graph paper, clearly write out the solution to each assigned problem, and CIRCLE YOUR ANSWER. You will be graded on your written solution—not only your answer—so be sure to SHOW YOUR WORK. You may write on both sides of the paper but don’t try to cram too much writing into a small space—spread out your work so it is easy to read and follow.
Math 1051 Lecture Section 10 Syllabus for Fall 2016 Page 11
To hand in a homework assignment, put the papers in order and staple them in the upper left corner. Write your HWID, your name and the homework number in the upper right corner of the first page of the packet of papers. Homework will be collected in the Tuesday discussion sessions and on exam days. Once it is graded, it will be returned to you in the discussion sessions.
On those days when we cover more than one section there will be more than one homework assignment. In those cases, staple your homework in separate packets, one for each assignment. This will help the grader with record keeping.
Hand in homework according to the schedule at the end of this syllabus.
Homework Grading: To receive full credit for homework and exam problems, you must show the mathematical steps necessary to solve the problems. Your written work is meant to “communicate” to us what you know about mathematics, not just the answers, so your work must be neat, organized, and complete. Each homework assignment will be worth a maximum of 5 points. Three points are for doing the problems from the textbook and 2 points are for correctly doing the review problems (numbered R02, R03, etc.). The problems are listed starting on page 16 of this syllabus.
Moodle Quizzes: On most lecture days, you will be required to complete a quiz outside of class on Moodle (Modular Object-Oriented Dynamic Learning Environment). These one-question quizzes will cover material from the lecture. They will open on the day of the lecture and close at 11:59 pm on Tuesday, Thursday, or Sunday. You must submit your solution within that time frame so be sure to start the quiz early enough to give yourself enough time to finish and submit it. Moodle will score the quizzes, tell you immediately how you did, and send your score to me. You will get 2 points for trying a quiz and an additional 3 points for getting the correct answer. These quizzes count for 5% of your final grade. The schedule of dates and topics is on page 16 of this syllabus.
Exams: The four 50-minute midterm exams will be closed book and notes. They will be done during a regular lecture class on the dates indicated on the schedule at the end of this syllabus. Keys for the exams will be posted on my web site after the exams are given. Because of the 50-minute time constraint, you must be very well prepared in order to work the problems in the time allotted. If you feel that you have a learning disability that would prevent you from doing your best within that time frame you should immediately contact the Disability Resource Center to see if they can authorize accommodations for you (such as extra time for exams). Information is available on their web site at https://diversity.umn.edu/disability/ by calling 612-626-1333 (for both voice and TTY), or by sending an email to [email protected].
The final exam will be on common final exam day, Fri 16 Dec, from 1:30 to 4:30 in a room to be announced in lecture and posted on my web site. The room will most likely NOT be our regular lecture room. If you don’t know where to go on final exam day call the School of Mathematics at 612-625-4848.
There will be no make-up exams. If you miss an exam you will be given a score of 0 until you take the final exam. At that time, your score on the final exam will be substituted for the 0. If you miss more than one exam you will get a score of 0 for the additional missed exams.
Page 12 Math 1051 Lecture Section 10 Syllabus for Fall 2016
Final Course Grade: The final grade for this course will be computed as follows:
Homework 15% Handed in at some Tuesday Discussion sessions and on exam days as specified on the schedule at the end of this syllabus.
Lecture work 5% Class work done in the MWF lectures.
PAL work 10% Class work done in the Thursday PAL sessions.
Moodle Quizzes 5% Completed outside of class after most lectures.
Exam #1 5% In-class exam covering the Appendix (review of high school algebra).
Exam #2 10% In-class exam covering Chapters 1 and 2.
Exam #3 10% In-class exam covering Chapters 3 and 4.
Exam #4 10% In-class exam covering Chapter 5.
Final exam 30% Exam covering the entire course. It will be on common exam day, Fri 16 Dec, from 1:30 to 4:30 in a room to be announced in lecture.
When I make out final grades I will replace your lowest exam score (including a 0 for a missed exam) with your final exam score if it is higher. Thus, if you completely blow one exam you can recover by doing well on the final exam.
Letter grades will most likely be assigned as follows:
Grade Total Points
A = 4.00 100 – 95 Represents achievement that is outstanding relative
A– = 3.67 94 – 90 to the level necessary to meet course requirements.
B+ = 3.33 89 – 86
B = 3.00 85 – 82 Represents achievement that is significantly above
B– = 2.67 81 – 80 the level necessary to meet course requirements.
C+ = 2.33 79 – 76
C = 2.00 75 – 73 Represents achievement that meets the course
C– = 1.67 72 – 70 requirements in every respect.
D+ = 1.33 69 – 68 Represents achievement that is worthy of credit even
D = 1.00 67 – 65 though it fails to meet fully the course requirements
S none 100 – 73 Represents achievement that is satisfactory.
F = 0.0 under 65 Represents a failure to meet course requirements.
N = 0.0 under 73 Represents a failure to meet course requirements.
Incompletes: Grades of I are normally not given in this course. However, they may be permitted due to extenuating circumstances for students who have completed most of the course and who are passing. In those cases a well-documented petition is required and the grade of I is subject to the approval of the Director of Undergraduate Studies of the School of Mathematics.
Math 1051 Lecture Section 10 Syllabus for Fall 2016 Page 13
Withdrawal: If you need to withdraw from the course, be aware of the following:
If you drop before the end of the second week of the semester no mention of the course will appear on your transcript; if you drop later, a W will appear on your transcript.
You may drop the course without permission before the end of the eighth week of the semester. After that date you cannot drop without permission of the instructor and the Director of Undergraduate Studies of the School of Mathematics.
Grades of W are subject to the conditions of your college and cannot be given if you take the final exam. If you find that you need to withdraw from the course contact me and your adviser immediately, don’t just stop coming to class!
Reports: Several times during the semester, progress reports will be emailed to your U of M Gmail account. If you use a different account, be sure to forward email from your U of M account to your preferred account. To do that log on to your U of M Gmail account, click the down arrow next to the gear (on the upper right) and select Settings. Click Forwarding and POP/IMAP. Click Add a forwarding address and follow the directions after that.
Student Conduct: The University seeks an environment that promotes academic achievement and integrity, that is protective of free inquiry, and that serves the educational mission of the University. Similarly, the University seeks a community that is free from violence, threats, and intimidation; that is respectful of the rights, opportunities, and welfare of students, faculty, staff, and guests of the University; and that does not threaten the physical or mental health or safety of members of the University community.
As a student at the University you are expected adhere to Board of Regents Policy: Student Conduct Code. To review the Student Conduct Code, please see: http://regents.umn.edu/sites/default/files/policies/Student_Conduct_Code.pdf
Note that the conduct code specifically addresses disruptive classroom conduct, which means "engaging in behavior that substantially or repeatedly interrupts either the instructor's ability to teach or student learning. The classroom extends to any setting where a student is engaged in work toward academic credit or satisfaction of program-based requirements or related activities."
Use of Personal Electronic Devices in the Classroom: Using personal electronic devices in the classroom setting can hinder instruction and learning, not only for the student using the device but also for other students in the class. To this end, the University establishes the right of each faculty member to determine if and how personal electronic devices are allowed to be used in the classroom. For complete information, please reference: http://policy.umn.edu/Policies/Education/Education/STUDENTRESP.html
Scholastic Dishonesty: You are expected to do your own academic work and cite sources as necessary. Failing to do so is scholastic dishonesty. Scholastic dishonesty means plagiarizing; cheating on assignments or examinations; engaging in unauthorized collaboration on academic work; taking, acquiring, or using test materials without faculty permission; submitting false or incomplete records of academic achievement; acting alone or in cooperation with another to falsify records or to obtain dishonestly grades, honors, awards, or professional endorsement; altering, forging, or misusing a University academic record; or fabricating or falsifying data, research procedures, or data analysis. If it is determined that a student has cheated, he or she may be given an "F" or an "N" for the course, and may face additional sanctions from the University. For additional information, please see: http://policy.umn.edu/Policies/Education/Education/INSTRUCTORRESP.html
Page 14 Math 1051 Lecture Section 10 Syllabus for Fall 2016
The Office for Student Conduct and Academic Integrity has compiled a useful list of Frequently Asked Questions pertaining to scholastic dishonesty: http://www1.umn.edu/oscai/integrity/student/index.html If you have additional questions, please clarify with your instructor for the course. Your instructor can respond to your specific questions regarding what would constitute scholastic dishonesty in the context of a particular class-e.g., whether collaboration on assignments is permitted, requirements and methods for citing sources, if electronic aids are permitted or prohibited during an exam.
Makeup Work for Legitimate Absences: Students will not be penalized for absence during the semester due to unavoidable or legitimate circumstances. Such circumstances include verified illness, participation in intercollegiate athletic events, subpoenas, jury duty, military service, bereavement, and religious observances. Such circumstances do not include voting in local, state, or national elections. For complete information, please see: http://policy.umn.edu/Policies/Education/Education/MAKEUPWORK.html
Appropriate Student Use of Class Notes and Course Materials: Taking notes is a means of recording information but more importantly of personally absorbing and integrating the educational experience. However, broadly disseminating class notes beyond the classroom community or accepting compensation for taking and distributing classroom notes undermines instructor interests in their intellectual work product while not substantially furthering instructor and student interests in effective learning. Such actions violate shared norms and standards of the academic community. For additional information, please see: http://policy.umn.edu/Policies/Education/Education/STUDENTRESP.html
Sexual Harassment: "Sexual harassment" means unwelcome sexual advances, requests for sexual favors, and/or other verbal or physical conduct of a sexual nature. Such conduct has the purpose or effect of unreasonably interfering with an individual's work or academic performance or creating an intimidating, hostile, or offensive working or academic environment in any University activity or program. Such behavior is not acceptable in the University setting. For additional information, please consult Board of Regents Policy: http://regents.umn.edu/sites/default/files/policies/SexHarassment.pdf
Equity, Diversity, Equal Opportunity, and Affirmative Action: The University provides equal access to and opportunity in its programs and facilities, without regard to race, color, creed, religion, national origin, gender, age, marital status, disability, public assistance status, veteran status, sexual orientation, gender identity, or gender expression. For more information, please consult Board of Regents Policy: http://regents.umn.edu/sites/default/files/policies/Equity_Diversity_EO_AA.pdf
Disability Accommodations: The University of Minnesota is committed to providing equitable access to learning opportunities for all students. Disability Services (DS) is the campus office that collaborates with students who have disabilities to provide and/or arrange reasonable accommodations.
If you have, or think you may have, a disability (e.g., mental health, attentional, learning, chronic health, sensory, or physical), please contact DS at 612-626-1333 to arrange a confidential discussion regarding equitable access and reasonable accommodations.
If you are registered with DS and have a current letter requesting reasonable accommodations, please contact your instructor as early in the semester as possible to discuss how the accommodations will be applied in the course.
For more information, see the DS website, https://diversity.umn.edu/disability/
Math 1051 Lecture Section 10 Syllabus for Fall 2016 Page 15
Mental Health and Stress Management: As a student you may experience a range of issues that can cause barriers to learning, such as strained relationships, increased anxiety, alcohol/drug problems, feeling down, difficulty concentrating and/or lack of motivation. These mental health concerns or stressful events may lead to diminished academic performance and may reduce your ability to participate in daily activities. University of Minnesota services are available to assist you. You can learn more about the broad range of confidential mental health services available on campus via the Student Mental Health Website: http://www.mentalhealth.umn.edu/
Here are some specific resources that can help you:
Boynton Health Service http://www.bhs.umn.edu/index.htm offers individual and couples counseling, urgent consultation, group therapies, medication assessment/management, social work assistance, and chemical health assessment/treatment. Hours are Monday 8 am to 6 pm, and Tuesday through Friday 8 am to 4:30 pm. Consultation about student situations is available by phone at 612-624-1444.
University Counseling and Consulting Service http://www.uccs.umn.edu/ offers both individual and group counseling for a range of concerns including academic difficulties, career exploration, and personal concerns. Walk-in hours for urgent student needs are Monday through Friday 8 am to 4:30 pm. Consultation about student situations is available by phone at 612-624-3323.
Disability Resource Center https://diversity.umn.edu/disability/ provides assistance with academic accommodations for students with diagnosed mental health conditions. Consultation regarding disability issues is available in-person or by phone 612-626-1333.
Office of International and Student and Scholar Services http://www.isss.umn.edu/ assists international students and scholars with many concerns, including stress and mental health issues. Confidential consultation is available at 612-626-7100.
Crisis/Urgent Consultation/After Hours Consultation is available 24 hours a day at 612-379-6363 or 1-866-379-6363 (toll free). If there is a life-threatening emergency, call 911.
Complaints Regarding Teaching/Grading: Students with complaints about teaching or grading should first try to resolve the problem with the instructor involved. If no satisfactory resolution can be reached, students may then discuss the matter with the Director of Undergraduate Studies, Professor Bryan Mosher, 117 Vincent Hall.
Academic Freedom and Responsibility: Academic freedom is a cornerstone of the University. Within the scope and content of the course as defined by the instructor, it includes the freedom to discuss relevant matters in the classroom. Along with this freedom comes responsibility. Students are encouraged to develop the capacity for critical judgment and to engage in a sustained and independent search for truth. Students are free to take reasoned exception to the views offered in any course of study and to reserve judgment about matters of opinion, but they are responsible for learning the content of any course of study for which they are enrolled.*
Reports of concerns about academic freedom are taken seriously, and there are individuals and offices available for help. Contact the instructor, the Department Chair, your adviser, the associate dean of the college, or the Vice Provost for Faculty and Academic Affairs.
And here we go! We are going to do the prep work needed for you to be successful in calculus, which is the mathematical study of change. Its founding ideas were developed by many people over many centuries but the two who are given the most credit for its formal development are Englishman Isaac Newton, who developed parts to solve problems in physics, which he most famously published in his Principia Mathematica, and German Gottfried Leibniz, who is considered an independent inventor of calculus and who developed much of the notation we use today. Newton is said to have developed his ideas first but Leibniz published his first.
Page 16 Math 1051 Lecture Section 10 Syllabus for Fall 2016
The homework review problems are on the next 5 pages. The schedule for Moodle quizzes follows that and the two pages after that contain a list of the assigned homework problems and the course calendar.
Math 1051 Review Problems
Homework is to be handed in for grading according to the schedule at the end of this syllabus.
Each homework assignment is worth 5 points, which will be awarded as follows:
For the textbook problems, you will earn 3 points if you have done them all and showed how you arrived at the answers. We understand that some problems can be done in your head so no work is needed for those, but most will require some algebra and for those your work must be shown. If you do some but not all of the problems you will be awarded 0, 1, or 2 points at the discretion of your DIS teacher.
The following review problems are also part of your homework. They are labeled Rxx, where xx is the corresponding homework number. For example, R02 is to be handed in with homework HW02. The problems will be graded by your DIS teacher who will award 2 points for a correct solution and answer, 1 point for a competent solution but the wrong answer (e.g., you made a simple arithmetic mistake), and 0 points for a poor solution or a correct answer that is not supported by the proper algebraic steps. Be sure to circle your answers.
The solutions will be posted on my web site http://www.z.umn.edu/robertson the day after they are due so you can check your work.
Tue 13 Sep
HW01 is a Diagnostic Pretest. Do problems on the key handed out in class.
There is no R01.
HW02 on Sec A.2 Geometry. Review problem R02 from Arithmetic.
1 5 1
Simplify:
12 18 10
HW03 on Sec A.3 Polynomials. Review problem R03 from Sec A.2 Geometry.
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