Math 1001 Survey of Math
Course Prerequisites
To succeed in this course you will need to have had two years of high school math.
Goals
This course provides an overview of mathematics as used in our society. A student who successfully completes this course will
- gain proficiency with mathematical models relating to a wide spectrum of real life situations, including scheduling, the traveling salesman problem, and personal finance.
- be able to critically assess these models, the assumptions inherent in the models, and their applicability to different situations,
- understand basic statistics and probability,
- understand symmetry, and identify symmetry in the world around them,
- understand tiling, and construct simple tilings,
- use a spreadsheet to analyze data and understand personal finance and other mathematical ideas.
Textbook
NOTE: TEXTBOOK EDITION IS ACCURATE FOR SPRING 2010.
The textbook for the course is For All Practical Purposes, 8th Ed., COMAP. The bookstore will have the latest edition, and the course calendar below is based on the 8th Edition. The differences between the editions is usually minimal, but if you use an earlier edition be aware that some of the sections may be numbered differently, content may be slightly different, and problems listed as practice below may not line up with your older edition. This is a very good book, in my opinion, but it certainly contains far more material than we will cover in this class. It should prove to be an excellent resource for you in the future. To be prepared for the lectures you should read the section the lecture is on before the lecture is given. I will typically not be able to cover everything from the section in the lecture, but I will indicate what material you are responsible for from each section.
Time Commitment
To succeed in this course you will need to be willing to spend, per week, nine hours outside of class reading the textbook and working problems (UMM policy is that one credit is defined as three hours of learning effort per week for an average student to earn an average grade in the course: 4 credits times 3 hours/week/credit - 3 hours/week in lecture = 9 hours/week outside class).
Course Components
Practice. On the course webpage I suggest practice homework problems for each lecture. You should do as much extra practice as you deem necessary to enhance your understanding of a topic. Falling behind in this course, as in any university course, can lead to disaster, so it is important that you keep up with the material. Practice problems are not graded.
Brain Builders. In class I will hand out short Brain Builders, which are exercises based on some of the concepts we are studying. Sometimes these Brain Builders will be completed and turned in during class, sometimes I will let you take them home and turn them in the following class. The Brain Builders should take about half an hour to complete. The course calendar below list tentative dates for the Brain Builders.
Assignments. Assignments will involve more complex problems than on the Brain Builders. Assignments will be handed out in class, and collected in class (the due dates are listed on the calendar below).
Assignments will be handed in at the beginning of class on the day they are due, unless you have spoken to me beforehand and I have granted an extension. Putting assignments in my mailbox or under my office door while I am teaching another course is severely frowned upon unless we have agreed that you will be doing this. If this is done when I am teaching your class I will not accept the work--believe it or not, people have actually done this!
I am demanding that solutions be written up well. This means solutions should be a self-contained document. They should be written legibly, contain diagrams or tables where appropriate, and should state the problem and explain the solution. Interspersing English sentences which explain what you are doing can help in this regard. With its worked-out examples, the book provides many examples of a good solution. To say it a different way, solutions with totally correct computations lacking in necessary good explanations will tend to receive 85%, not 100%.
It is OK to collaborate on assignments, and I anticipate many of you will work with other students in the class, however, every student turns in their own solutions to all the problems on each assignment. Collaboration does not mean that others do your thinking for you. Collaboration in this course means there is a good back and forth conversation among study partners, but never direct copying of another's work. For example, if a study partner gets stuck on a problem, you should help them get unstuck by telling them in words what it was that you did to get past the part they are stuck on. Using words instead of showing them your work is important, since they will then have been provided a hint but will still need to do the work themselves. This facilitates learning, which simply copying your work will not. If in helping a classmate you get to the point where you think you need to show them your work for them to be able to answer the question, don't show them your work--it is time for them to come visit office hours.
Excel. Excel is a component of some assignments, and each student will create their own Excel-based solutions when these are asked for. Basically, you should not work two people to one computer--if two people are working on separate computers they can talk with each other if they get stuck, but each person creates their own solution, and that is what I want. Do not leave copies of your assignments on public computers! Copy them to your own disk and then delete them from the Recycle Bin before you leave a public computer.
Exams. You will not be allowed any outside material on your desks during these exams. You will need a calculator that can do exponents (23=8 for example) for some of the problems on the tests and final. Debriefing after tests should be done during office hours, after you have had a chance to reflect on the exam.
Grading
Here is the University-wide uniform grading policy.
- A Represents achievement that is outstanding relative to the level necessary to meet course requirements.
- B Represents achievement that is significantly above the level necessary to meet course requirements.
- C Represents achievement that meets the course requirements in every respect.
- D Represents achievement that is worthy of credit even though it fails to fully meet the course requirements.
- F Represents failure and indicates that the coursework was completed but at a level unworthy of credit, or was not completed and there was no agreement between the instructor and student that the student would be temporarily given an incomplete.
The grade for the course will be calculated by the following formula:
| Brain Builders | 20% |
| Assignments | 45% |
| Tests | 35% |
Your numerical grades will be converted to letter grades and finally Grade Points via the following cutoffs (see the UMM Catalog for more on Grades and Grading Policy):
| Numerical | 95% | 90% | 87% | 83% | 80% | 77% | 73% | 70% | 65% | 60% | Below 60% |
| Letter | A | A- | B+ | B | B- | C+ | C | C- | D+ | D | F |
| Grade Point | 4.00 | 3.67 | 3.33 | 3.00 | 2.67 | 2.33 | 2.00 | 1.67 | 1.33 | 1.00 | 0.00 |
Respectful Classroom
- Be in class on time. I nor you fellow classmates enjoy the disruption late arrival causes. I know that situations crop up that will entail late arrival (please come even if you are late!) but try to ensure it is the exception and not the rule.
- If you need to leave class early, let me know before class and slip out as unobtrusively as possible.
- During class, cell phones and music devices should be turned off, and headphones removed from ears.
- To ask a question during class, you can get my attention by saying my name (``Barry, could you explain how you know the graph has an Euler circuit?") or raise your hand.
- 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 or reduce a
student`s ability to participate in daily activities.
If you have any special needs or requirements to
help you succeed in the class, come and talk to me as soon as
possible, or visit the appropriate University service yourself.
You can learn more about the range of services available on campus by visiting
the websites:
- The Academic Assistance Center www.morris.umn.edu/services/dsoaac/aac/
- Student Counseling www.morris.umn.edu/services/counseling/
- Disability Services www.morris.umn.edu/services/dsoaac/dso
- Multi-Ethnic Student Program www.morris.umn.edu/services/msp/
- Cooperation is vital to your future success, which ever path you take. I encourage cooperation amongst students where ever possible, but the act of copying or other forms of cheating will not be tolerated. Academic dishonesty in any portion of the academic work for a course is grounds for awarding a grade of F or N for the entire course. Any act of plagiarism that is detected will result in a mark of zero on the entire assignment or test for both parties. If you are in any way unclear about what constitutes academic dishonesty, reread the earlier section on Assignments where I discuss collaboration, and please come and talk to me if you have any questions. UMM's Academic Integrity policy and procedures can be found at www.morris.umn.edu/Scholastic/AcademicIntegrity/.
- Since the assignments are handed out days in advance, only under exceptional circumstances (which can be officially documented) will I accept late work. You will receive a mark of zero if an assignment is submitted late. However, please talk with me asap (do not wait until the next class) if you missed turning something in, even if it is after the deadline.
- If you are going to miss an exam, let me know in advance so we can work out alternate plans. Taking an exam early can usually be arranged.
Lecture Preparation
The majority of your learning will take place outside of lectures, as you work problems and read the text. You will not learn everything you need to learn in this course simply by coming to lectures, nor if you miss lectures. You must come to lectures and put in the time outside of class to master the material. To get the most out of the course you should
- work on homework
for the course every day.
I can not stress enough how important it is that you work problems! The homework identifies the types of problems from the text that should be mastered. - read the section before the lecture
and do not fall behind.
Make sure when you are reading that you are reading for comprehension. This means you are thinking about what you are reading, rereading paragraphs when necessary, and pausing to work through examples to ensure you understand them completely. Make notes about the material, especially anything you don't fully understand. Then come see me, your study group, or a tutor to discuss these concepts so that you do understand them. Reading for comprehension takes practice, but it is an essential skill to develop to help you succeed at university. As you read, try to focus on understanding rather than memorization. - discuss any difficulties with me during office hours, or by appointment,.
Please make the most of my Office Hours! When you come to office hours, come prepared: for conceptual questions bring your notes on the topic and any problems you have done relating to that topic; for homework questions, bring the work you have done on that problem. - form a study group.
Exam Preparation
Here are some suggestions to guide your preparation for tests. If you have a technique which works for you and isn't listed here, please let me know so I can pass it on to your peers!- Review assignments and homework solutions. This will provide you with an overview of the material you need to be studying.
- Review the concepts and vocabulary in the text. Can you talk about the concepts? Do you know the basic results from the concept review?
- Make notes on the topics you are studying as you review. Write short sentences to describe how to solve problems. Describe verbally to a friend how you would solve a particular type of problem. This verbal description will help you remember the process of solving particular problems during the test.
- Do problems from the text which have solutions that are similar to problems seen in class or assigned as homework.
- Branch out and do other types of problems that appeared less frequently throughout the section.
- Studying in many short sessions is more effective than one or two marathon studying sessions. Consider making a time schedule which maps out when and what you will study. You might choose a long term time frame (Friday Morning: History, Friday Afternoon: Precalculus, etc), and a short term time frame for each day that lists what exactly you will focus on. The short term time frame can be created every day and be more flexible. Create goals which you can reasonably be expected to meet.
- Get as much sleep as possible while you study for tests. Come to your exams well rested, and mentally sharp.
- Study in an environment that mimics the environment the test will take place in. It should be quiet and clear of clutter.
- Use the practice tests questions provided on the course webpage as a practice test, maybe only doing a selection of the problems so it is a bit shorter. Answer these questions as if you are taking a test, without the textbook or any other resources that will not be provided on the test.
- For a given chapter (or section), create practice "tests" for yourself, maybe three or four questions which you have the solution to, and then answer them without reference to the text. Correct your test yourself, or work with a friend and have them correct your test and you correct theirs. Do not move on to other questions until you have mastered these ones. You might consider imposing a time limit on these mini-tests.
- If you do study in groups, also study alone so you can focus on the types of questions you need to work on.
- Come and talk with me (email me to set an appointment if necessary) if there are questions you have.
Course Calendar
Here is the tentative lecture schedule. You are responsible for any changes to this schedule which are announced in class.
| # | Date | Notices | Topic | Practice | Concepts/Resources |
|---|---|---|---|---|---|
| 1 | Jan 19 | Course Introduction Chapter 1: Urban Services Graph of Cyrus |
3,4,17,18,21,29 Euler Circuits |
graphs (vertex, edge, path, circuit), Euler circuit, valence, connected graph Sand Drawings |
|
| 2 | Jan 21 | Brain Builder 1 | Chapter 1: Urban Services Chapter 2: Business Efficiency 310,224,200,866,619,719,680,000 |
Ch 1: 31,33,41,56 Eulerizing a Graph Ch 2: 1,3,5,9,13,21 |
eulerizing a graph, digraph, optimal solution,weight, complete graph, Hamiltonian circuit, minimum-cost Hamiltonian circuit, method of trees, counting, Saying Big Numbers |
| 3 | Jan 26 | Chapter 2: Business Efficiency Using Kruskals Algorithm to Create Mazes How Short a Shortcut? & Stamp |
33,35,37,47,49,51,59,63
Nearest Neighbour Alg. Sorted Edges Algorithm Kruskal's Algorithm |
nearest neighbour algorithm, sorted edges algorithm, trees, spanning tree, minimum cost spanning tree, TSP Java Applet, Kruskal's algorithm, Java Applet for Kruskal's Algorithm | |
| 4 | Jan 28 | Ass. 1 Due | Chapter 2: Business Efficiency Chapter 3: Planning & Scheduling ORD Examples |
Ch 2: 68,72 Ch 3: 5,7,11,13,17,25 |
order requirement digraph, scheduling and schedules, list processing algorithm, critical path scheduling, independent tasks, decreasing time list algorithm |
| 5 | Feb 2 |
Chapter 3: Planning & Scheduling Bin Packing Example |
43, 47, 55, 5765,75 Vertex Coloring Scheduling |
bin packing algorithms, Review of Scheduling, vertex coloring, chromatic number,
Map Coloring Resource for Teachers The Four Colour Theorem: History A More Mathematical Discussion New Proof |
|
| 6 | Feb 4 | Ass. 2 Due | Chapter 4: Linear Programming | Ch 4: 1,5,7,9,21,27,31 | Interactive Demo, Graphical Solution to System of Linear Inequalities, constraints, the feasible region, the corner principle |
| 7 | Feb 9 | Brain Builder 2 | Chapter 4: Linear Programming feasible region and the profit |
Example (Excel File), FYI: Solving LP problems with Excel | |
| 8 | Feb 11 | Test on Chapters 1-4 | Test 1 Practice | Solution | ||
| 9 | Feb 16 | Meet in IH 11 | Excel Workshop in Imholte 11 Section 1: Introduction to Using Excel Spreadsheets |
ExcelIntro.xlsx (Excel 2007 format) Guide for Excel 2003 and OpenOffice |
|
| 10 | Feb 18 | Brain Builder 3 | Chapter 5: Exploring Data: Distributions Histograms for Health Insurance (Excel) (data) Boxplots for Construction Wages (Excel) |
5,7,11,21,23,29 Histogram Example Old Faithful |
distributions, numerical summaries, histograms (shape center, spread, outlier, symmetric, skewed), stemplots, mean, median, quartiles, five number summary, boxplots, variance, standard deviation, Application of Boxplots |
| 11 | Feb 23 | Chapter 6: Exploring Data: Relationships Excel File on Regression |
3,5,11,23 Correlation and Regression |
scatterplots (response & explanatory variables, form, direction, strength), regression lines, correlation, Regression Applet, Sample Data Sets | |
| 12 | Feb 25 | Meet in IH 11 | Excel Workshop in Imholte 11 Section 2: Analyzing Data Using Excel |
data1.txt | data2.txt | |
| 13 | Mar 2 | Meet in IH 11 | Excel Workshop in Imholte 11 Exploring Data |
chance to work on Assignment #3 | |
| 14 | Mar 4 | Ass. 3 Due | Chapter 8: Probability: The Math of Chance Dice Experiments |
1,5,7,9,13,17,25,27 | probability, sample space, event, probability rules, probability model for a finite sample space, Rolling Dice, the mean of a probability model, law of large numbers, The Fair Dice, The Fair Dice (interactive but flaky), Even More Dice |
| 15 | Mar 9 | Brain Builder 4 | Chapter 8: Probability: The Math of Chance | 33,35,37,39 | normal distributions, probability as area under curve, mean, standard deviation, 68-95-99.7 rule, central limit theorem |
| 16 | Mar 11 | Test on Chapter 5,6,8 | Test 2 Practice | Solution | ||
| Mar 16 | Spring Break | ||||
| Mar 18 | Spring Break | ||||
| 17 | Mar 23 | Chapter 21: Saving | 1,3,5,11,12,13 | simple and compound interest, arithmetic and geometric growth, terminology, continuous compounding (exponential function, e) | |
| 18 | Mar 25 | Brain Builder 5 | Chapter 21: Saving | 17,21,31,33 | accumulation, savings formula, terminology, exponential decay, inflation, depreciation, Consumer Price Index |
| 19 | Mar 30 | Meet in IH 11 | Excel Workshop in Imholte 11 Saving: What Excel file should look like |
chance to work on Assignment #4 | |
| 20 | Apr 1 | Ass. 4 Due | Chapter 22: Borrowing | 1,15,19,23,25 | simple and compound interest, conventional loans, amortize, amortization calculator, home equity, Interest Only Loans |
| 21 | Apr 6 | Meet in IH 11 | Excel Workshop in Imholte 11 Borrowing: What Excel file should look like |
chance to work on Assignment #5 | |
| 22 | Apr 8 | Ass. 5 Due | Chapter 23: Economics of Resources Population Growth Models (Excel) |
7,9, 11, 13, 15,21, 21, 23, 25, 41 | Arithmetic, Geometric, Logistic Grow; population doubling; How long nonrenewable resources last, Sustaining renewable resources, cobweb diagrams, chaos |
| 23 | Apr 13 | Test on Chapter 21-23 | Test 3 Practice | Solution | ||
| 24 | Apr 15 | Chapter 19: Symmetry and Patterns Fibonacci Sequence (Excel) |
1,7,9, 21, 23 | Golden Ratio, Fibonacci, Fibs blog, rigid motions, golden rectangle and aesthetics | |
| 25 | Apr 20 | Brain Builder 6 | Chapter 19: Symmetry and Patterns Strip Patterns |
Ch 19: 33,37 | notation for patterns strip pattern used in class |
| 26 | Apr 22 | Chapter 19: Symmetry and Patterns Group Theory |
27,49,54,55 | Symmetry Group for Equilateral Triangle,
Group for Equilateral Triangle FYI: Group Properties of Integers FYI: Groups in Chemistry |
|
| 27 | Apr 27 | Chapter 19: Symmetry and Patterns Fractals and Chaos Movie: Fractals - Hunting the Hidden Dimension |
Ch 19: | BU Fractals and Chaos: Zooming Sierpinski | |
| 28 | Apr 29 | Chapter 20: Tilings | |||
| 29 | May 4 | Chapter 20: Tilings | Ch 20: 1,3,12 | regular polygons, regular and semiregular tilings, tilings with irregular polygons Web Resources: Tesselations Interactive Tessellation Tool Marjorie Rice |
|
| 30 | May 6 | Ass. 6 Due | Chapter 20: Tilings | 27,29,30 |
Escher, tiling by translations, tilings by rotations and half turns. Web Resources: Interactive Tesselate Totally Tesselated: Escher, M. C. Escher Home Page, Escher and Droste Effect |
| May 10 11:00am-1:00pm | Final Exam on Chapters 19,20 | Test 4 Practice | Solution | |||
