mathematics finite mathematics homework help

mathematics finite mathematics homework help

Exploring the Principles and Applications of Finite Mathematics

1. Introduction to Finite Mathematics

In conclusion, the main difference between mathematics lies in the emphasis placed on applications. In this lesson, we usually study both useful problems, applied methods, and general theories. Finite mathematics can have some relationships between it and statistics, which are both studies of applications. This lesson provides a general introduction to the field of finite mathematics. In the field of practical philosophy, finite mathematics is math with finite means, symbols by which to represent finite numbers. Depending on the definition of the number, finite mathematics studies the finite attributes of numbers, quantities, structures, and functions, such as whether the properties of finite structures can be used to determine the properties of infinite structures.

The field’s first course that the non-specialist is likely to encounter is finite mathematics. One of the key phrases of finite mathematics is ‘practical applications’, and indeed, this lecture will contain many. This is certainly true, and students in finite mathematics and elementary statistics bring with them a wide variety of backgrounds and, not surprisingly, pursue a number of different majors and fields of study. The focus is on real-world applications and methods, theories, and logic from algebra, calculus, and other fields of study that students have not yet encountered have largely been abolished from the textbooks. Finite mathematics is a very theoretical field, and much of finite mathematics is not concerned with practical problems. Its emphasis is on theory. However, finite mathematics is also used in other fields with particular interests. Finite mathematics majors may, on the side, study interesting problems and theorems in graph theory, combinatorial theory, and enumeration, set theory, and other fields of software that are not usually the main focus of study.

2. Key Concepts and Techniques in Finite Mathematics

When dealing with the first chapter of finite mathematics, set theory is discussed and presented as a free-standing environment. A set is essentially a collection of objects, which are referred to as elements. Four ways of describing sets are presented, after which several special sets are discussed. Each of the previous components introduces a unique and relatively simplistic Chapter 2 concept, allowing for simple geometry or graph applications on real and natural numbers before students are asked to combine different Chapter 2 techniques in a single example. Chapter 4 hits upon how combinations can be used to judge the national draft lottery as a clear application. In this case, organizations utilized probability to better explore a fairly absurd outcome.

Chapters in Finite Mathematics 1. Introduction: Exploring Life in the Mathematical World 2. Set Theory: Using a Unique Notation to Describe the Members of a Collection 3. Combinatorics: Counting the Elements of a Collection 4. Probability: Determining the Likelihood of an Event’s Occurrence 5. Matrices: Utilizing Tools for Solving Certain Types of Systems of Equations 6. Linear Programming: Solving a Special Case of an Optimization Problem 7. Graph Theory: Investigating Transportation Problems Using Simple Graphs

The field of finite mathematics includes an incredibly diverse set of principles and techniques, each of which contributes to a better understanding of the world around us from a mathematical perspective. Herein, we review the primary chapters and topics that generally make up a course in finite mathematics, including such crucial chapters as set theory, combinatorial techniques, probability, systems of linear equations, matrices, linear programming, and graph theory. A short discussion of the techniques and problem-solving strategies used in each of these chapters also follows.

3. Applications of Finite Mathematics in Real-world Scenarios

I discussed global shipping, airlines, and quick-service delivery companies with examples. At the beginning of the first month, during 1996, a large global transporter minimizes transportation costs. The company runs delivery trucks for 20 businesses on a daily basis in 10 towns, each potentially each day with two to eight requests. Cutting routes would increase the max given by 10 but would also reduce some businesses’ guaranteed deliveries to 50 or eight or six per day. More than 5,100 distinct path mix calculations led to a useful method of product demand for customers, reduction of travel time each mile by truck, reduction of gasoline operating expenses by 13%, and continues an expected annual transport cost reduction of at least 9%.

Finite mathematics applications exist mostly in the domains of textbooks, but they are practiced professionally and utilized extensively in a variety of broader topics in science, business, finance, and various related applications of science and machinery. As a business ethic, I strive to study decisions about scarcity in the theory primarily benefiting the business employee, the boss or operator, and subsequently the customer in the enterprise. I noted this originally with mathematical models and some real-world case studies in the mid-1980s. Examples of primary real-world occurrences include applications in loss minimization of utility monitoring, site testing, insurance risk minimization, and personal financial decisions. Many more problems I’ve examined and described in classes, in publications, or in government and industry meetings and seminars since this idea was spread.

4. Solving Problems and Exercises in Finite Mathematics

x=4.

interval 0-134 ; 400+5-x, 10-92, x +0, 492, 892, 314. Solve for x: 4x+52

Solutions To count the 4-place numbers using the digits 0, 1, 2, 3, 4, 5, 6: 3, 360.

3. Find the number of 4-place numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6 if repetitions of digits are allowed. 4. Determine the number of sets in the n1 ∩n2 ∩n3 that contain exactly one straight-line S. 5. Draw a Venn diagram that accurately represents the following sets: A={0, 1, 2, 3, 4, 5}, B={2, 4, 6, 8}, and C={0, 3, 6, 9}. 6. A school club has 33 members. This prompts an investigational committee to decide the number of combinations of students that can be paired if club members are combined in pairs. Determine the number of combinations. 7. Find the indicated function. 8. A clerk divides up a bundle of letters for mailing. Twelve letters are left over if they are bundled in groups of three, six remain if bundled in groups of four, and three remain if bundled in groups of six. Determine the least number of letters. 9. Graph and plot the ordered pair(s) of the parabolas. 10. How many triples of boys can be formed from a 15-member group if there is no restriction on the selection? Addendum.

4.2. Exercises Solve the following exercises. 1. A box contains four red, four white, and four black balls. A person draws three balls from the box. Find the probability that the balls drawn are red, white, and black, respective. 2. A wheel of fortune that has a section for each digit shows only the digits zero through eight. The wheel of fortune is spun; if one digit in any particular section is drawn from the wheel, what is the probability that the digit drawn is less than or equal to three?

4.1. Problems 1. A box contains four red, four white, and four black balls. Six balls are chosen at random from the box. Find the probability that four are red and two are black. 2. Find the number of 3-place symbols that can be formed from the digits 1, 2, 3, 4, 5 if repetition of digits is excluded but where each symbol is to be even. 3. A person throws four tickets out a window, where there are ten students standing. The probability that the same two students both get a ticket at the first two tries and that the other two students both get tickets at the third try is a. 0 b. c. 4. Show that 1, 6, 14, and 24 are the only products of consecutive prime numbers n(n + 1). 5. Using the following sets N={1,2,3,…,8,9,10}, A={1,3,5,7}, B={2,4,6,8}, and C={5,6,7,8,10}, find (a) AC and (b) A ∪C. 6. Let members of a club have periods listed 1, 2, 3, 4, 5, 6. If the club is combined in pairs, show the results (1 2), (1 3), (1 4), (1 5), (1 6), (2 3), (2 4), (2 5), (2 6), (3 4), (3 5), (3 6), (4 5), and (4 6). Determine a value, n, so that (4 6) is the n-th such pair. 7. Let functions f(x) and g(x) subject to the given conditions find the indicated function for the given (The constant of integration can be ignored.):(a) f(x) f'(x), f(1) = -2 ; g(x) x * g'(x),(b) f(x)=2\(\sqrt{x}\) +4, g(x) =x(3+7x). 8. A man has 4 true five-dollar gold pieces, 2 fake five-dollar gold pieces, and 7 fake gold-plated nickels in his pocket. Three coins fall out and clink noisily on the ground. Find the probability they are identical. 9. Find the area of the region that is common to the parabola \(y=\frac{x^{2}}{4}+1\) and the line x+3y=12 \(\sqrt{9-2x}\). 10. How many selections can be made from the letters of the word “triangle” that have exactly three vowels?

5. Conclusion and Further Resources

In general, the practical application of the mathematics discussed in the essay is somewhat limited due to the brevity of coverage. A wealth of references exploring finite mathematics in more detail is available for further reading. Full information on these perspectives may be found in any of the standard references which investigate the application of finite mathematics to calculation in trading markets. Another area where discrete mathematics is already used to great advantage and is likely to grow in importance is the field of computer and information science. There are many references available on particular topics such as probability and Markov Chains; for a list of references allowing varying levels of study, see the bibliography in Introduction to Probability. For a more thorough treatment of discrete mathematics, see Lipson. To explore problem-solving in a variety of contexts, “The Art of Problem Solving” by Zeitz is a well-regarded text.

In conclusion, the study of discrete structures and their quantitative aspects is known as the study of finite mathematics. There are several areas of life and scientific pursuit in which knowledge of finite mathematics is essential in order to be able to function competently. As you can see, retiring wealth over time is as much the application of finite mathematics as is the computation of bank interest or the throwing of darts. Solving problems arising in areas like business, science, medicine, communication, or the internet requires similar problem-solving techniques as solving the problems posed in our examples.