Act Utilitarianism Versus Kant s Principle Of Ends Essay

Act Utilitarianism versus Kant’s Principle of Ends. Introduction There are many theories out there when it comes to any kind of ethics. I will be discussing Act Utilitarianism and Kant’s Principle of Ends. Both are good theories, but they do have their differences. I think that how we perceive either of these depends on how we were brought up by our families and what we believe in when it comes down to making decisions. While both are similar theories they are also different in their own way. All of my research on this paper I pulled from our book â€Å"Ethical Choices† 2011. Theories, Pros, Cons and Opinion Act Utilitarianism is the morally right act, for any situation, is that act which produce the greatest overall utility in its consequences. (â€Å"Ethical Choices† 2011). Act utilitarians believe that we need to understand what is right and what is wrong in order for us to make ethical decisions. In doing so, it tells us what we ought to do to promote the greatest amount of utility. In this view, we are focused on the scope, duration, intensity and probability of our actions. The scope tells us how many people are affected by certain actions; The duration tells us the amount of time that the effects our actions last; Intensity tells us how differently people are affected by our actions in that no two situation affect people the same; and, The probability tells us that we can’t predict our futures, but we can estimate how are actions affect others. In act utilitarianism weShow MoreRelatedKant And The Moral Law1451 Words   |  6 PagesIntroduction: Kant argues that mere conformity with the moral law is not sufficient for moral goodness. I will argue that Kant is right. 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How My Writing Has Improved - 1515 Words

After this semester of English 102, at Bristol Community College I feel that I have gained the skill to articulate what I want to convey to the reader in many ways. I don’t just look at grammatical error, but instead I look for ways to make my sentences more effective and concise. Nevertheless, I hope that this strategy will continue to help me improve my writing even further on in the future. My strong points as a reader have also definitely improved after reading the poems and stories we experienced this semester. Writing has been an important form of expression for me. I find myself to be very soft spoken and speaking verbally is usually difficult for me because I can’t always seem to find the right words to say. I feel that I am more expressive and have more control over what I want to say. While this semester progressed toward its end, I have learned new writing skills and gradually learned how to engage with audiences. This skill was very useful in meeting my course goals in English 102. I believe that I have grown at organization and careful stream my thoughts as well. Before I would just begin writing my papers without any plans or organization, along with no definite idea of where I would be going with the assignments, but throughout this course I’ve learned that you should base your paper around your thesis statement. Another skill I took from this class was to value my classmate’s responses, from their reactions made me much more aware that my main ideasShow MoreRelatedHow My Writing Has Improved Greatly Improved After Taking English 103928 Words   |  4 Pagesterm â€Å"writing†, they don’t really associate this with a single course that they have taken in high school or college. Rather, most people view â€Å"writing† as a process that evolves as we become capable of thinking in more abstract manners. 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Applications of Discrete Mathematics free essay sample

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in continuous mathematics such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been haracterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the integers, including rational numbers but not real numbers). However, there is no exact, universally agreed, definition of the term discrete mathematics. Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions. The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete athematics that deals with finite sets, particularly those areas relevant to business. Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete athematics to real-world problems, such as in operations research. Although the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed as well. Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term discrete mathematics is therefore used in contrast with continuous mathematics, which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete bjects can often be characterized by integers, continuous objects require real numbers. The study of how discrete objects combine with one another and the probabilities of various outcomes is known as combinatorics. Other fields of mathematics that are considered to be part of discrete mathematics include graph theory and the theory of computation. Topics in discrete mathematics Complexity studies the time taken by algorithms, such as this sorting routine. Theoretical computer science includes areas of discrete mathematics relevant to computing. It draws heavily on graph theory and logic. Included within theoretical computer science is the study of algorithms for computing mathematical results. Computability studies what can be computed in principle, and has close ties to logic, while complexity studies the time taken by computations. Automata theory and formal language theory are closely related to computability. Petri nets and process mathematics are used in analyzing VLSI electronic circuits. Computational geometry applies algorithms to geometrical problems, while computer image analysis applies them to representations of images. Theoretical computer science also includes the tudy of continuous computational topics such as analog computation, continuous computability such as computable analysis, continuous complexity such as information-based complexity, and continuous systems and models of computation such as analog VLSI, analog automata, differential petri nets, real time process algebra. Information theory The ASCII codes for the word Wikipedia, given here in binary, provide a way of representing the word in information theory, as well as for information-processing algorithms. Information theory involves the quantification of information. Closely elated is coding theory which is used to design efficient and reliable data transmission and storage methods. Information theory also includes continuous topics such as: analog signals, analog coding, analog encryption. Logic Logic is the study of the principles of valid reasoning and inference, as well as of consistency, soundness, and completeness. For example, in most systems of logic (but not in intuitionistic logic) Peirces law is a theorem. For classical logic, it can be easily verified with a truth table. The study of mathematical proof is particularly important in logic, and has applications to automated theorem proving nd formal verification of software. Logical formulas are discrete structures, as are proofs, which form finite trees[8] or, more generally, directed acyclic graph structures[9][10] (with each inference step combining one or more premise branches to give a single conclusion). The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false, but logic can also be continuous-valued, e. . , fuzzy logic. Concepts such as infinite proof trees or infinite derivation trees have also been studied,[11] e. g. infinitary logic. Set theory Set theory is the branch of mathematics that studies sets, which are collections of objects, such as {blue, white, red} or the (infinite) set of all prime numbers. Partially ordered sets and sets with other relations have applications in several areas. In discrete mathematics, countable sets (inc luding finite sets) are the main focus. The beginning of set theory as a branch of mathematics is usually marked by Georg Cantors work distinguishing between different kinds of infinite set, motivated by the study of trigonometric series, and further development of the theory of infinite sets is outside the scope of discrete mathematics. Indeed, contemporary work in descriptive set theory makes extensive use of traditional continuous mathematics. Combinatorics Combinatorics studies the way in which discrete structures can be combined or arranged. Enumerative combinatorics concentrates on counting the number of certain combinatorial objects e. g. the twelvefold way provides a unified framework for counting permutations, combinations and partitions. Analytic combinatorics concerns the enumeration of combinatorial structures using tools from complex analysis and probability theory. In contrast with enumerative combinatorics which ses explicit combinatorial formulae and generating functions to describe the is a study of combinatorial designs, which are collections of subsets with certain intersection properties. Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to q-series, special functions and orthogonal polynomials. Originally a part of number theory and analysis, partition theory is now considered a part of combinatorics or an independent field. Order theory is the study of partially ordered sets, both finite and infinite. Graph theory Graph theory has close links to group theory. This truncated tetrahedron graph is related to the alternating group A4. Graph theory, the study of graphs and networks, is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right. [12] Algebraic graph theory has close links with group theory. Graph theory has widespread applications in all areas of mathematics and science. There are even continuous graphs. Probability Discrete probability theory deals with events that occur in countable sample spaces. For example, count observations such as the numbers of birds in flocks comprise only atural number values {O, 1, 2, . On the other hand, continuous observations such as the weights of birds comprise real number values and would typically be modeled by a continuous probability distribution such as the normal. Discrete probability distributions can be used to approximate continuous ones and vice versa. For highly constrained situations such as throwing dice or experiments with decks of cards, calculati ng the probability of events is basically enumerative combinatorics. Number theory The Ulam spiral of numbers, with black pixels showing prime numbers. This diagram ints at patterns in the distribution of prime numbers. Main article: Number theory Number theory is concerned with the properties of numbers in general, particularly integers. It has applications to cryptography, cryptanalysis, and cryptology, particularly with regard to prime numbers and primality testing. Other discrete aspects of number theory include geometry of numbers. In analytic number theory, techniques from continuous mathematics are also used. Topics that go beyond discrete objects include transcendental numbers, diophantine approximation, p-adic analysis and function fields. Algebra Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: boolean algebra used in logic gates and programming; relational algebra used in databases; discrete and finite versions of groups, rings and fields are important in algebraic coding theory; discrete semigroups and monoids appear in the theory of formal languages. Calculus of finite differences, discrete calculus or discrete analysis A function defined on an interval of the integers is usually called a sequence. A sequence could be a finite sequence from some data source or an infinite sequence from a discrete dynamical system. Such a discrete function could be defined explicitly by a list (if its domain is finite), or by a formula for its general term, or it could be given implicitly by a recurrence relation or difference differentiation by taking the difference between adjacent terms; they can be used to approximate differential equations or (more often) studied in their own right. Many questions and methods concerning differential equations have counterparts for difference equations. For instance where there are integral transforms in harmonic analysis for studying continuous functions or analog signals, there are discrete ransforms for discrete functions or digital signals. As well as the discrete metric there are more general discrete or finite metric spaces and finite topological spaces. Geometry Computational geometry applies computer algorithms to representations of geometrical objects. Main articles: discrete geometry and computational geometry Discrete geometry and combinatorial geometry are about combinatorial properties of discrete collections of geometrical objects. A long-standing topic in discrete geometry is tiling of the plane. Computational geometry applies algorithms to geometrical problems. Topology Although topology is the field of mathematics that formalizes and generalizes the intuitive notion of continuous deformation of objects, it gives rise to many discrete topics; this can be attributed in part to the focus on topological invariants, which themselves usually take discrete values. See combinatorial topology, topological graph theory, topological combinatorics, computational topology, discrete topological space, finite topological space. Operations research Operations research provides techniques for solving practical problems in business and other fields † problems such as allocating resources to maximize profit, or cheduling project activities to minimize risk. Operations research techniques include linear programming and other areas of optimization, queuing theory, scheduling theory, network theory. Operations research also includes continuous topics such as continuous-time Markov process, continuous-time martingales, process optimization, and continuous and hybrid control theory. Game theory, decision theory, utility theory, social choice theory I Cooperate I Defect I Cooperate | 1-10,0 1 Defect 10, -10 1-5, -5 | Payoff matrix for the Prisoners dilemma, a common example in game theory. One player chooses a row, the other a column; the resulting pair gives their payoffs I Decision theory is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision. Utility theory is about measures of the relative economic satisfaction from, or desirability of, consumption of various goods and services. Social choice theory is about voting. A more puzzle-based approach to voting is ballot theory. Game theory deals with situations where success depends on the choices of others, which makes hoosing the best course of action more complex. There are even continuous games, see differential game. Topics include auction theory and fair division. Discretization into discrete counterparts, often for the purposes of making calculations easier by using approximations. Numerical analysis provides an important example. Discrete analogues of continuous mathematics There are many concepts in continuous mathematics which have discrete versions, such as discrete calculus, discrete probability distributions, discrete Fourier transforms, discrete geometry, discrete logarithms, discrete differential geometry, iscrete exterior calculus, discrete Morse theory, difference equations, and discrete dynamical systems. In applied mathematics, discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, discrete formulae are fit to data. A common method in this form of modelling is to use recurrence relations. Hybrid discrete and continuous mathematics The time scale calculus is a unification of the theory of difference equations with that of differential equations, which has applications to fields requiring simultaneous modelling of discrete and continuous data.