Professional Connections With Discrete Mathematics

Discrete mathematics can be viewed as a set, or collection, of a number of concepts spanning algorithms, logic, matrix operations, and set theory. Basic applications of these concepts can seem fairly clear as you study them, while the further translation, or transfer, in applicability to the real world or to your profession can be harder to grasp without focused research and reflection. This discussion is an opportunity for you to market yourself to a prospective employer by presenting how the concepts and skills you have learned in this class may be applied to your current or future profession.

Post 1: Initial Response

You will write a college-level learning narrative in which you write specifically about how the skills and concepts you have learned in class are useful to a current or future employer. Choose two specific concepts or skills that you have studied in this course and research how they may be applied to your current or future profession. You will highlight specific examples related to each concept as evidence of your learning and express key ideas related to each concept which you discover are important in your field based on evidence from your research.

As you draft the body paragraphs of your learning narrative, address the following questions for each of your two concepts:

How is the concept applicable to the field you would like to pursue?

From your research, what sources discuss this application, and how do they characterize applying the concept in the profession?

Share at least one specific example of a problem or skill you learned to show your prospective employer your understanding of this concept.

Share at least two key ideas that you need to highlight during an interview.

Is knowledge of the concept reflected in the required skills for a job advertisement you might consider? If so, describe the job and what part of the job advertisement reflects the need to possess knowledge of this concept.

The learning narrative should include a title page and reference page, as well as at least 1-page double-spaced in 12-point Times New Roman font. Every piece of writing should have an introduction, body, and conclusion. You are expected to use outside resources for this essay. Cite at least two sources in proper APA format on a reference page. You must also use appropriate APA in-text citations throughout your narrative.

Your writing should include a highly developed purpose and viewpoint; it should also be written in Standard English and demonstrate college-level content, organization, style, grammar, and mechanics. There should be no evidence of plagiarism.

Im gonna just post some units we went over in class an you can choose any of them. Im going to school for Inormation Technology with a focus on security. Im currently a nurse. You can choose whatever and how to associate it the concepts with.

During Unit 1, you will explore the foundational mechanics of computing with your study of logical reasoning. Logic, commonly associated with the idea of making sense, is a branch of mathematics with much greater depth and history. From ideas debated by philosophers to symbolic forms agreed upon and codified by mathematicians over centuries, you will be exposed to the use of symbolic logic connectives to build complex statements. You will explore how to analyze a complex statement with a truth table to determine the truth or falsehood of the statement based upon the simple statements, or inputs, in its construction. In doing so, you will also be able to assess different complex statements for logical equivalence by comparison of their truth tables. The application of these concepts extends to the field of digital logic in how computers communicate and store information. The logical analysis of true and false statements has connections to the use of zeros and ones in machine operations with binary numbers.

NUMBER SYSTEMS

An effective computing system starts with putting a solid foundation in place, such as with sufficient random access memory (RAM) and hard-disk space. The same is true, on a granular level, with systems of numeration for which the computer can operate efficiently. While you may find it efficient to make everyday determinations with base 10 values, which date back to before written history when humans counted using their fingers and toes, the binary system lends itself naturally to efficient computer operation. Given that computers at their rudimentary level process data in two possible states, on and off, binary representations using zeros and ones serve as the fundamental building blocks of computation.

In Unit 2, you will explore various number systems, anchoring your study in the familiar decimal, or base 10, system. Also known as the Hindu-Arabic system, you have used the decimal system throughout life for everyday communications, for example when you want to express the number of hours you need to complete a project or to add up the amount owed to a friend after eating out a few times. After examining how base-numeration works in detail, using the decimal system, you will apply the same processes to understand the binary, base 2, and hexadecimal, base 16, systems which are used by computers. You will also have the opportunity to explore operations on binary numbers as well as express and compute quantities using modular arithmetic, a tool particularly applicable to encryption.

Unit 3 COUNTING TECHNIQUES

Ever wonder how many different bank PIN numbers could be created for a 4-key code? How many different inputs the user of your software program might use to achieve some desired output? Or, what are the total number of data breach possibilities you need to prepare for in developing your company’s database security protocol?

In this unit, you will have the opportunity to explore the use of counting techniques to address questions like those above or to explore some personal curiosity! For example, how many ways can you order a pizza with three toppings from your local pizza shop? Could you even try them all within a year, eating one option a day?

By gaining confidence in how you interpret a given situation and evaluate the number of possible outcomes, you can be well prepared for what to expect. From an operations perspective, the use of mathematical counting principles can yield insight into how many outcomes you will need to consider and prepare for in the completion of a project.

Unit 4 PROBABILITY

In this unit, you will navigate the variety of ways in which probability may be used to understand the likelihood of future events. How are weather forecasts determined? How do technicians determine the likelihood a system’s security will be compromised? Based on the project or task you are approaching, you may be best informed by the use of theoretical probability models in some situations and by gathering empirical data to understand likelihood in other situations.

You will further apply probability to determine the expected values of certain events. For example, given the probability various subscribers will opt-in to paid usage of your app at various price points, what might you expect to earn over the next 100 or 1,000 downloads? This evaluation method, expected value, is foundational to decision processes that you can apply in weighing your options in real-world settings — both personal and professional.

Unit 5 SEQUENCES, SERIES, AND ALGORITHMS

In this unit, you will be introduced to mathematical sequences and series as well as their connections to algorithms. In addition, you will examine algorithm efficiency, broadly, by considering qualities such as iteration and operation count.

How do apps or programs run? How do coding professionals determine whether an algorithm can be improved? Through applications involving sequences and the theory of algorithm efficiency, you can understand the answers to these types of questions. No matter what industry you consider, step-by-step formulas or processes (algorithms) and methods for examining their efficiency will always be valuable tools.

Unit 6 SET THEORY

In this unit, you will be introduced to set theory and how it can be applied to modeling and understanding the relationships among data attributes in relational databases or the organization of objects. Suppose you administered a survey and collected response data. How are respondents to the survey alike? How are they different? Through observation of their responses, you can subset the data and understand similarities and differences among the respondents to help inform a marketing or policy decision.

You will further apply set theory in performing operations on sets, for instance taking their unions or intersections. You will also visualize set relations using Venn diagrams. Visualizations, such as with Venn diagrams, can create impact if you are presenting information to an audience or team. For example, suppose you found that the intersection, or common attribute, among the majority of orders placed over the past month with your company was that they were placed within the first week of the month. This could be key knowledge to present to your team to plan for when to send out marketing or place advertisements.

Unit 7 GRAPH THEORY

In this unit, you will begin a two-unit study of graph theory (sometimes called network theory), a valuable field of modeling real-world phenomena that can be reduced to easily interpretable graphing norms. Suppose you want to establish a sequence of connections between servers such that you ensure the return of data to the original hub. Establishing the relationships among all of the servers communicating with a central hub (e.g., a cloud storage database) is where graph theory can become particularly useful. Graphs can help you visualize and organize the relationships among various objects to optimize and plan for ongoing management.

You will explore how to define a graph using vertices and edges. Then, you will examine a variety of interpretations one can draw from a graph, starting with simple paths, for example in sending data from a server to a tower to a phone in the context of cellular data transfer. You will practice identifying trails and circuits within a graph, determining the degree of a vertex, and assessing whether specific types of trails or cycles exist within a graph, such as a Euler trail or a Hamiltonian cycle. As an IT professional, you might be tasked with planning the design of a cloud-based server network or mapping efficient routes for sending data to a cellphone user in real time. The use of graph theory can make projects or working protocols remarkably more efficient!

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