Discrete mathematics

Coming into UNC as a first-year student, I was lucky enough to have quite a few transfer credits from high school; many of which were in my intended field of study: mathematics. Looking to continue with a major in mathematics, I signed up for the next course in the intended major progression, MATH 381: Discrete Mathematics. This course serves as an introduction to mathematical logic, almost like a stepping stone towards higher mathematics. On my first day of my first year at Carolina, I walked into the classroom in Phillips to realize that I was the only first year in the course. The rest of them were sophomores or juniors, who were all quite familiar with the inner machinations of Carolina’s mathematics department. Despite the courses and…

In this paper, the author has explained how mathematics can be taught to software engineering students. It is important for software engineering student to know mathematical foundation and techniques to solve problems. Mainly the foundation contained logic and discrete mathematics and techniques that author explained are specification and reasoning. The specification is a process in which informally given concepts are transformed into mathematical model and theory. The reasoning is the process…

Proof is incorporated in the VCE Mathematics Study Design 2016-2018 and VCE Mathematics textbooks. Proof is integrated in many areas of study such as arithmetic and number, geometry measurement and trigonometry, algebra and structure, and discrete mathematics (Victorian Curriculum and Assessment Authority [VCAA], 2016). This supports the idea that one of the central goals of school mathematics, notably at the upper secondary level, is the development of proof concepts (Coe & Ruthven, 1994).…

The importance of this is that if children are able to complete a valid proof, it shows they have an understanding of problem and if they have been able to prove a conjecture, it does in turn show a deeper understanding in mathematics (Goldberger, 2002). The quality and variety of language that pupils hear and speak are important factors in presenting a mathematical proof (Department for Education, 2013), children gain knowledge from one another therefore discussion is used to build secure…

Over the past years, scientists from different fields, extending from medicine and biology to applied mathematics and computer science, have teamed up to assess emerging diseases. Mathematical modelling plays an important role in predicting, forecasting and controlling disease outbreaks. Despite control measures, it often happens that outbreaks remain a serious public health risk in areas where recurrent outbreaks have been observed for a long time. Therefore, it is crucial to evaluate the…

Approaching junior year, I remained uncertain regarding my upcoming course choices. I had taken Math III during the previous semester and felt confident in my math abilities when reflecting upon the course. I knew I needed one more math credit, but I did not know if I should sign up for Honors Discrete Mathematics or Honors Precalculus. Knowing I would face a Calculus class while in college, I decided to take Honors Precalculus, not knowing the challenge that awaited me. Consequently, I…

In observing other students trying out along with me (similar to the teachers who observed Maria in chapter 8), it has been valuable to see how they handle these misconceptions and the whole process has been eye-opening with regards to the number of things to consider in my own planning for these “mock” teaching scenarios.Turning to the article on functions by NCTM, I was reminded of my own mathematics learning experiences in middle and high school. I feel as if my understanding of functions…

touched on in some of the most ancient mathematical texts from Egypt , dating from over a thousand years earlier. One of the simplest proofs comes from ancient China, and probably dates from well before Pythagoras' birth. It was Pythagoras, though, who gave the theorem its definitive form, although it is not clear whether Pythagoras himself definitively proved it or merely described it. Either way, it has become one of the best-known of all mathematical theorems, and as many as 400 different…

Review of the mathematical paper Introduction The article that is reviewed today is “An introduction to mathematics of HIV/Aids modelling” by Leigh Johnson published in 2004 for Centre of Actuarial Research for University of Cape Town, South Africa. The article provides an introduction to modelling HIV/Aids transmission as well as survival and focuses on children who lost their parents due to HIV/Aids called orphans. The lack of proper Introduction to the article isn’t easily allowing the…

Thus, when a house has been burglarized before, it increases the attractiveness value for the house and those nearby. Criminals move toward areas of high attractiveness values. If no additional burglaries occur in the vicinity, the attractiveness decreases. Mathematical modeling of crime in general, and burglaries in particular, is based on the “broken window effect” or repeat victimization sociological effect, which implies that houses in areas of past burglaries have a higher chance of being…