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Objectives

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Learning Objectives for MATH M118

Learning mathematics is a complex job, but it is not an impossible one. We hope that laying out these course goals and objectives will be helpful to you.

  • You will learn some basic terminology.
  • You will learn and practice reasoning and mathematical computational skills. We will show you how to get started, and we will show you examples, but most of your learning will come from practice.
  • You will adopt some attitudes. You will not be graded on these, but we put them on the list for two reasons. (1) Because having the these attitudes will be to your advantage in meeting the other objectives (2) Because having these attitudes will be to your advantage in the rest of your education and in your professional career.

Terminology

Chapter 1

 Logic  Statement  Truth Value  Compound Statement
 Negation  Conjunction  Disjunction  Premise
 Conclusion  Conditional  Biconditional  Tautology
 Contradiction  Valid Argument  Contrapositive  Converse
 Inverse      

Chapter 2

 Set  Element  Roster Method  Set-Builder Notation
 Infinite Set  Finite Set  Cardinal Number  Empty or Null Set
 Subset  Set Equality  Universal Set  Complement
 Union  Intersection  Disjoint Sets  Relative Complement
 Partition  Venn Diagram  De Morgan's Laws  Cartesian Product

Chapter 3

 Sample Space  Tree Diagram  FCP  Factorial
 Permutation  Indistinguishable  With Replacement  Circular Permutation
 Combination  Pascal's Triangle  Unordered Partitions  

Chapter 4

 Equally Likely Outcomes  Properties of Probability  Addition Rule of Probability  Conditional Probability
 Binomial Probability  Independent Events  Bayes Theorem  Disjoint Events
 Bernoulli Trials  Odds For an Event  Odds Against an Event  

Chapter 5

 Mode  Median  Mean  Random Variable
 Probability Density Function  Expected Value  Standard Deviation  Normal Distribution
 Z-score      

Chapter 6

 System of Equations  Consistent and Inconsistent Systems
 Dependent and Independent Systems  Gauss-Jordan Elimination Method
 Matrices and Echelon Tableaus  Reduced Echelon Tableau Form
 Pivoting and Main Diagonal  Row Equivalent Operations
 Identity and Coefficient Matrix  Row and Column Vectors
 Transpose of a Matrix  Adding and Multiplying Matrices
 Scalar Product  Inverse of a Matrix
 Closed and Open Input-Output Model  Production and Demand Matrix

Chapter 7

 Linear Program  Constraints  System of Linear Inequalities  Redundant Constraints
 Corner Point  Bounded Region  Degenerate Point  Solution Set
 Convex Region  Objective Function  Feasible Region  Nonnegativity
 Unbounded Region      

Chapter 8

 Simplex Algorithm  Objective Function  Slack Variables  Structural Variables
 Nonnegativity Constraints  Structural Constraints  Feasible Solution  Basic Variables
 Nonbasic Variables  Dual Program  Crown's Method  Mixed Constraints

Chapter 9

 Markov Process  Markov Chains  States  System
 Transition Matrix  Transition Diagram  State Vector  Irreducible
 Regular Markov Chain  Absorbing Markov Chain  Absorbing State  Transient State
 Steady State Vector      

 

Skills

Read and understand an English language description of a problem. You will learn to determine what physical quantities and processes are involved. You will learn to determine which quantities you may presume to be known, which may be neglected, and which you are responsible for determining.

Analyze the problem. Most problems cannot be solved in a single step. You will learn to break problems down into subproblems that can each be solved independently. You will learn to recognize which laws are relevant, and you will learn to apply the laws to solve the subproblems. You will also learn to reassemble these solutions into a solution to the whole problem.

Describe the problem. In order to break down the problem and reassemble the solution efficiently, you will learn to describe the problem in several useful ways. You will learn to use appropriate diagrams, graphs, mathematical formulas and terminology to describe problems and solutions in a way that emphasizes the physics and suppresses the complexities and ambiguities of everyday language.

Explain your results. The last link in this chain is to take your solution, which is usually in a mathematical form, and restate it in English. Taken together, these first four skills are what we call "problem solving."

Organize your knowledge. Like most college courses, there is a lot of material covered in this class. You will learn to recognize how this knowledge fits together to make a whole subject.

Picturing situations. In physics, we often deal with complex situations in which several objects interact. You will learn to picture these situations as a step towards analyzing them.

Modeling. This is a complex skill, which we will only begin to teach you. The idea is to take complicated real-world situations and create models of those situations that are useful. To be useful a model must be simpler than the real thing: enough so that it can be analyzed. But the model cannot be too simple. It must reflect the aspects of the situation that make it worth studying.

Connecting your knowledge. You will learn how physics is connected to other courses you have taken, to other areas of knowledge, and to knowledge you have gained informally ("common sense").

Attitudes

Remember that knowledge is cumulative.
Many technical subjects are structured like a pyramid. Each idea is built on the foundation of the last. Therefore, you cannot forget a formula or idea just because the test is over. That idea may be vital to your understanding of something new next week, next month, or next semester. Learn this subject for life.

Be bold.
We all know this is a difficult subject, and sometimes you will just be clue less. That is ok, it happens to all of us, faculty included. If you do not understand something, ask a question in a big room in a loud voice. The lecture hall is ideal. Remember the saying "the only stupid question is the one not asked." In a similar vein, turn in every homework assignment, even if it is all wrong. Turning in incorrect work looks bold. Not turning it in looks lazy.

Persevere.
At times, you may feel like we are asking too much, or that the material is just too hard. At these times, you need to suck it up and work extra hard. Put in an extra hour working problems, take an extra hour to talk to one of the faculty, whatever it takes. We try to make sure everyone succeeds in this course. However, we also want you to reach as far as you can. Everyone's ability should be stretched by this course. It isn't supposed to be easy.

Get serious.
When you are doing something difficult, you need to use all your skills, and you need to devote plenty of time. Organize you work so you don't loose things. Do all the assignments. Use every resource available, that includes faculty office time, the library, the internet, and other students. Do every assignment as if you were going to frame it. If it is going to be difficult, you want to be able to brag about it later.

Be curious.
Ask yourself why we are studying each idea, concept, formula, etc. Mathematics is one of the most finely tuned subjects in the undergraduate curriculum (This isn't ego, it is age. Mathematics is simply an older subject). Everything in the course is there for a reason. If you can figure the reason out, you will learn something about the way the subject is structured, and that will help you succeed. If you can't figure it out, ask.

Be skeptical
When you finish a problem, be prepared to back it up. Ask yourself "how can I prove this is correct"? There are ways to do this (checking units, testing limits, etc.); we will demonstrate in class. When you use these methods, you help yourself by looking at the problem in new ways, and by examining how it fits with other ideas. Also, backing up your ideas is an extremely useful skill in the workplace. Practice now.

 

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