Trough Real-Word Applications

Learning Mathematics

Trough Real-Word Applications

SYLLABUS

An introduction to contemporary mathematics I

MAT129.1 ID 3276

FALL 2015

Lecturers:

Enver Atamanov, Kandidat nauk in Physics and Mathematics, Acting Professor,

Class meetings: 3 classes per week, 15 working weeks.

Office hours: according to faculty schedules. Office: 415

Course description:

This course introduces you to a variety of mathematical subjects and makes you think about the nature of mathematics itself. You will study a number of approaches to contemporary mathematics: linear algebra, analytic geometry, linear programming, mathematical models in finances and mathematical analysis. You will learn to think like a mathematician and to apply mathematical principles to everyday life and scientific study. You will come to see how the mathematical objects can be used to design elegant models that alter the way we think and enable the development of new knowledge. We hope that you will enjoy exploring beautiful mathematical ideas!

Prerequisite: secondary school mathematics.

Textbooks:

1.  Linda Gilbert, Jimmie Gilbert. College Algebra. Trigonometry. 1986.

2.  Mizrahi A., Sullivan M. Mathematics for business and social sciences.-John Wiley &Sons.1988.

3.  Margaret L.Lial, Charles D.Miller. Finite mathematics and calculus with applications. -Scott, Foresman and Company. 1989.

4.  Grossman. Calculus of one variable. Academic Press. Inc.1986.

5.  Edwards and Penney. Calculus and analytic Geometry. Prentice Hall Inc. 1986.

6.  Larson R.E., Hosteller R.P. Brief Calculus with applications. D.C. Heath and Company. 1987.

7.  Howard L. Rolf. Finite mathematics. Baylor University. Inc. 2005.

8.  All materials are presented on electronic resource of AUCA: H:\Courses Information Support\Natural Sciences and Information Technologies\MAT 128 An Introduction to Contemporary Mathematics I.

Objectives:

The primary objectives of this course are:

•  to develop abstract and logical (probative) thinking

•  understanding how to set and solve problems

•  acquiring as basic knowledge of contemporary mathematics

•  appreciating the value of continued mathematical education for the major

Expected outcomes:

After completing MAT 129.1 students will be able to

•  recognize universal mathematical objects in real life and in various sciences;

•  formulate laws for mathematical objects using the main factors and omitting the minor ones;

•  having a basic knowledge of Linear Algebra, Analytic Geometry, Linear Programming, Financial Mathematics and Mathematical and Mathematical Analysis.

Method of Evaluating Outcomes:

Grading

Tests are graded by a team of faculty. To ensure consistency each team member grades the same question(s) on each test. Students may appeal the grading of a test question on a designated appeal day (time and room to be announced). Students may discuss any problem with the faculty member who graded their work and state the reason for the appeal. Only the grader determines whether any adjustment to the grade should be made. Students should discuss the appeal with the course instructor who will then make any necessary adjustment to the record and return the paper to the department office.

Grades will be based on a total of 100 points:

Quiz 1 / The lecturer sets day and time / 10 points
Midterm Exam / The lecturer sets day and time / 25 points
Quiz 2 / The lecturer sets day and time / 10 points
Final Exam / The lecturer sets day and time / 35 points
Home works / Every class / 20 points

The total grade of the student is as follows:

0 £ F £ 40 D £ 45 C- £ 50 C £60 C+ £65 B- £70 B £ 80 B+ £ 85 A- £ 90 A£100.

Make-up Exams and Quizzes

·  If the reason for missing the Midterm Exam is valid, the student’s final exam will be worth up to 50 points. In this case extra tasks will be included in the final test.

·  If the reason for missing the Final Exam is valid, the student may retake the Final Exam at another time assigned by the department. In this case the Final Exam will be worth a maximum of 25 points. A student can also apply for the grade of “I”.

·  If a student misses both exams, he/she will not be attested for the course.

·  If a student has missed Quiz 1 for a valid reason, the student may take Quiz 1 at the time specified by the lecturer before Midterm Exam. If a student misses the Quiz 2 for a valid reason, the student may take Quiz 2 at the time specified by the lecturer before Final Exam.

Attendance Requirements

It is important to attend classes to master the materials in the course. Attendance affects grades: students lose 1 point for any unexcused absence.

Academic Honesty

The Mathematics and Natural Sciences Department has zero tolerance policy for cheating. Students who have questions or concerns about academic honesty should ask their professors or refer to the University Catalog for more information.

Workbooks

Each student must maintain a math workbook with a clear record of completed homework. Workbooks will be assessed from time to time. Students should bring their workbooks to all classes as they are necessary for their class work. Workbooks must be submitted for assessment immediately upon request of the instructor or full credit for homework may not be earned. The workbook must contain calculations completed by the student. Photo-copies of answers will not be accepted nor will answers that have been copied from the back of the text book or transcribed from the solution manual. We highly recommend working jointly with your fellow students on homework problems.

Calculators

Students will be advised whether calculators are needed for specific assignments. Graphic calculators may not be used during quizzes and exams.

Cell phones

We ask students to turn off their cell phones during math classes. Use of cell phones is entirely prohibited during the exams.

Syllabus change

Instructors reserve the right to change or modify this syllabus as needed; any changes will be announced in class.

Tentative Academic Calendar:

Weeks 1-4.

Many applications in business, social, and biological sciences represent information in tables or rectangular arrays of numbers (matrices). Matrices are mathematically interesting because they can be used to represent a system of equations. Systems of linear equations model situations reasonably well. We will provide simple examples of how to use systems of linear equations. We are using Gauss-Jordan techniques to solve a system of equations.

·  Data analysis. Least square problem. Cryptography (coding and encrypting message). Mathematical toolkit: Matrix algebra. [1]: p.376-382. Exercises [1]: p. 382-383. [2]: p. 65-81.

·  Supply and Demand, Market Price. Problems of Quantity and Cost. Mixture Problem. Investment Problem. Mathematical toolkit: Systems of linear equations. [1]: p. 397-401. Exercises [1]: p. 401-402. Gauss-Jordan techniques. Gaussion Elimination Method [1]: p.387-390. [2]: p. 56-64. Exercises [1]: p. 391-392.

Weeks 6-7.

In many physical problems we are interested in the relationships between variable quantities. In this section we discuss two methods for describing such relationships: analytical, by means of formulas, and geometric, by means of graphs. We will discuss graphs and functions from the very beginning so that we all have a common understanding. Among other things, we will learn to recognize equations whose graphs are straight lines. This material has numerous important applications.

·  Prediction in Economics (Least square problem). Simple interest. Supply and Demand. Geometrical interpretation of the linear equations system. Mathematical toolkit: Cartesian coordinate system on the plane. [2]: p. 13-16. Distance between two points on the plane. Segment division. The straight line on the plane. [2]: p. 16-30. Equations of the straight line. Exercises [2]: p. 30-32. Parallel and intersecting lines. [2]: p. 3-42. [3]: p. 162-190

Week 8. Preparation for the Midterm Exam

Weeks 9-11.

The term linear programming refers to a precise mathematical procedure that will solve certain types of optimization problems that involve linear conditions in form of equations and inequalities. If, for example, a company would like to maximize performance and productivity, then it needs to answer such important questions as “How can we achieve the most efficient production?”, ”How can we obtain maximum profit?”, “What personnel and equipment are needed to complete the project on time and hold costs to a minimum?” These questions determine the best strategy or procedure that should be implemented. The solutions to such problems are called optimal solutions. Some of these problems can be solved with a linear programming. Today, linear programming helps determine the best diets, the most efficient production scheduling, the least waste of materials used in manufacturing, and the most economical transportation of goods.

·  Optimum production output. Diet problem. Transportation problem. Optimal use of land. Investment strategy. Mathematical toolkit: Linear function of two variables. Linear inequalities. A geometric approach to linear programming problems. [1]: p. 142-186.

Weeks 12-13.

·  Functions and their graphs [2]: p. 415-451.

·  The derivative. Optimization problems. Application to economics [2]:p. 477-487, p.596-602, p.604-611.

Weeks 14-15.

Good mathematical models are often versatile and flexible, and the financial models used in this section apply broadly to important life problems. The financial models to be considered are based on mathematical concepts of progression and difference equation and the corresponding theory describing its properties

·  Mathematical models in finances. Simple Interest and simple Discount. Compound Interest. Annuities. [1]: p. 721. Present Value of an Annuity. Amorttization. Mathematical toolkit: Arithmetic Growth (progression) and Simple Interest. [1]: p. 679. Geometric Growth (progression) and Compound Interest [1]: p. 681.

Communication is an important activity of the human race, but it is often difficult. We sometimes have difficulty expressing our thoughts. We make statements that another person interprets in a way we did not intend. To be sure that no question arises about the meaning, we sometimes ask lawyers to draw up a document to convey the precise intention of the information in the document. Even so, a lawsuit may arise when two parties disagree on the meaning and intent of the document. Because problems in clear and precise communication do exist, mathematicians have sought to study these problems in order to clarify them and make some areas of communication more precise. In this topic we introduce you to this area of mathematics- mathematical logic.

Week 15. Preparation for the final exam

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