Mathematics Essays

His interest in statistics was much provoked by a talk which Abe Girshik made on the sequential analysis, and that changed the way that Blackwell visualized sampling. The everyday practice where scientists limit their samples before they started working; on this, Abe Girshik proposed that scientists sample until they see enough.

The fact that Isaac Newton had arrived at his discoveries earlier, between 1665 and 1666 but failed to publish them is indisputable. On the other hand, the fact that Gottfried Leibniz published his discoveries on calculus earlier than Isaac Newton, between 1674 and 1684, before Newton published his inventions in 1687 is also indisputable. 

The historical and social context of Riemann’s short life is promptly recognized. Riemann was born to a pastor of Breselenz near Dannenberg in the kingdom of Hanover on 17 September 1826. He went to gymnasiums in Hanover (1840-1842) and in Luneburg (1842-1846) and studied at Gottingen (1846-1847, 1849-1851) and at Berlin (1847-1849).

Further, annualized growth rates were plotted against the benchmark level of per-capita income. The methodology followed for this is plotting the graph for the whole period (1950-2010) and other for 1975-1984 and 1985-1996. The plot shows a vertical axis measuring log of the annualized growth against period (T) for the horizontal axis.

The motion of bacteria like Escherichia coli is similar to a random walk problem, the motion is a “smooth run” interspersed by brief tumbling periods during which the bacterium chooses a new direction. The bacterium moves away from repellents or towards attractants by modifying its tumbling frequency.

Conventional wisdom dictates that boys are better than girls in science subjects and mathematics. While no scientific proof is available to verify this claim, empirical evidence sways between approving this claim and at the same time disapproving it by showing that there is no difference in performance across the gender divide.

The Nine Chapters' whole designation on Mathematical Art is presented on two bronze typical measures dated 179 CE. However, there are claims that the book existed before in various titles. According to intellectuals, Chinese mathematics and ancient Mediterranean world mathematics had evolved more or less unconventionally.

Many real-life situations also need statistics therefore it is important to learn these skills so as we can have solutions to our daily problems. As we have seen statistics can also help in the prediction of the future hence it is of very great importance in avoiding future problems by taking precautions after being warned by statistics. 

Taguchi method entails the reduction of process variations through the design of experiment processes that are robust. This method was brought about by Taguchi who came up with a method for the design of experiments that was aimed at investigating how various process parameters impact the variance and mean characteristics for process performance.

From the findings, it will be noted that the generated numbers are from the uniformly distributed populations as shown by the frequency test. The run test shows that the numbers are not biased and they come from the population. The gap test shows that the random number is independent as there value is smaller than the critical value. 

In Fyrileiv and Collberg's (2005) study, they observed that the effective axial force was the virtual force achieved through the stresses’ integral over the steel cross-section. The effective axial force, according to the authors, can be described as a concept utilized for avoiding the pressure effects integration over the surfaces of double-curves.

Because of a consensus that exists among practitioners and researchers that early childhood at the year between 2 and 4 of school is an essential period for school readiness, educators of these children believe that learning of mathematics in the form of the fraction is very essential (Wright & Stafford, 2000). 

If the mental images and relationships to which the student is trying to connect new knowledge are poorly developed, future constructs are weak and confused, and misconceptions may arise. Secondly, if students can execute a procedure but do not have understanding, it is impossible that they will use this knowledge when required in a new situation.

When put into observation, only some assortment managers count constraints of this type in their optimization structure. Instead, an average mean-variance optimization quandary is solved and then, in a “post-optimization” step, engendered portfolio weights or trades are pruned to convince the restraints.

As a maths teacher, I acknowledge the importance of technology in simplifying tasks and enhancing efficiency. I strongly believe that children should be taught how to use various technological platforms while they are still young. In order to realize this, it is important to incorporate technology into different learning activities.

The second over expectation design, however, did not turn out as expected. It was expected that if F was inhibitory, it would pass the summation test when it was paired with G. F did not seem to be inhibitory as the GF outcome values were 51.7 which were higher than those of G, 49.97 (F did not pass the summation test).

Reasoning: Students are required to demonstrate their abilities and capacity to logically think and act, analyze and evaluate mathematical problems, infer and justify their answers, and explain how they arrived at the answer. Reasoning extends to the comparison and differentiation of different mathematical concepts, transferring learning to other areas and explaining their choice of formula or method.  

The essay discussed how interests in trigonometry led to the progress of the prominent area of study in mathematics. It was argued that studies in trigonometry could be traced back to Egyptian, Babylonian, and Greek mathematics. The essay argued that the desire to know more about trigonometry motivated mathematicians to study more.

Ranging from the population, earth’s orbit, sunspot across the skies, and climate/ weather, this method of prediction has been very handy in solving a lot of issues that are beyond human control. Climate for example is easily predictable through values that can be modeled to give an overview of what is expected.

Math anxiety significantly contributes to poor performance in mathematics among learners across the world. There are many factors that contribute to math anxiety including teacher biases and poor teaching practices, parent stereotyping, peer influence, and misguided individual lack of interest and support. 

Symptomatic infected persons’ treatment with drugs and chemoprophylaxis will be positive in lowering an epidemic. Drug treatment carried out on symptomatic infected persons will only benefit this group and will have little impact on the epidemic. The predictions of the model point out the necessity of getting better drug efficacy estimates. 

Letting u and v become the concatenation input-strings and be denoted by * then the inputs u and v will be similar in a manner of Nerode, denoted by u ~ v, when u and v are concatenated with the similar arbitrary-string w and the outcome of the outputs are similar despite the value of w. Let f be the output/input map. 

In conclusion, Lattice problems may not entirely be assumed to be hard as there has been no any quantum algorithm that can perform better than the classical algorithm of lattice. This knowledge serves an important aspect in the communication systems, where we would want data or information that is transmitted to be protected. 

Encryption takes place to make plain text unreadable by unauthorized personnel. This is done by having a key and an algorithm which will achieve it. The key represents the number of positions a letter will have to be shifted. To increase the security of this we can increase the length of the key and device more complex algorithm. 

By definition, a network condition is a condition in which a variable stands for a lattice. There is a wide range of routes in which frameworks can be utilized as a part of unraveling condition to fluctuating degrees of accommodation and application. One of the courses is to utilize what is called Jordan Normal Form (JNF). 

A wave function is described as a variable quantity that mathematically describes the wave characteristics of a particle or mathematically describes a system quantum state. A wave function of a particle has value and the value at a given space and time is related to the possibility of that particle present in that space at that time.

The t (time) presents the time an oscillation takes to complete a single cycle. The cycles may include the vibrations as well. Damped harmonic motion presents the oscillation that is resistant to the motion where the friction or force applied is proportional to the velocity. Given in F fricition = -C dy / dt.

The probability density function tends to determine the distribution of the discrete random variable. For random variables that are continuous, CDF is properly defined so as we could provide the CDF. PMF is not applicable for the continuous random variables since for the continuous random variable P (X=x) is always perceived to be 0.

The incorporated circuits are significantly created on silicon chips which are slashed from silicon wafers. The manufacture of wafers experiences a number of strides that decide the chips that will be fruitful. Through the Czochralski procedure where gems are developed, silicon wafers are delivered and inserted circuits are exchanged to the wafers by the lithographic process.

If f represents a function and G is the graph and the function taking the integer which is positive f(v) of the vertices V  v(G). When this is taken in the G edges, it deems to be a coloring off coloring. The f chromatic index indicates the minimum number of colors that are needed in the f color of G. This is represented as Xf’ (G). 

For quartics with one inflection point, it will not possible to find a ratio as for calculating ratio we need to have two inflection points Q and R. however, in this case, there will be one. For quartics with two inflection points, of which one or two are horizontal the ratio will be again Golden ratio.

Comparing the NPVs of both products. The NPV of product X (considering a 10% discount, without a discount, the NPV can not be computed) is £459,325 whereas the NPV of product Y is £464,530. The NPV of product Y is slightly greater than that of product X. So product Y is slightly better in terms of NPV.

The comparison between weight and height indicates that the smaller in weight and shorter in size players who assume the backs position perform better in both their scoring and defending. When BMI is applied in this situation, it divides weight on the basis of height while at the same time neutralization the relationship between weight and height.

For instance, if π was represented as a decimal number and expanded to its billionth decimal place, would the occurrence of 200,000 1s or 2s within this representation mean that π is a regular or non-normal irrational number? While considering normality and non-normality of irrational numbers, π and e have been numerically represented to more.

Mathematics is a wide field. It entails a number of topics that range from algebra, geometry, statistics, and probability to business mathematics. These topics are a reflection of real-life circumstances. For instance, probability as a topic is used in lottery games where one has to select a single number or chance out of the many provided options. 

The payoff functions stand for each player’s favourite over action profiles. An action profile is a list of actions, one for each player. Pure-strategy Nash equilibrium is an action profile with the feature that no single player can attain a higher pay off by conflicting unilaterally from this profile.

An Egyptian fraction is any fraction that can be expressed as the sum of separate unit fractions. The Egyptian fractions are of the form where n is an integer. The ancient Egyptians used to write these fractions in specially-designed papyrus reeds. They used to squash and press the reeds into long scrolls of paper that could easily be carried.

In order to conduct a successful study, a researcher needs to understand how the experiment should be carried out. The researcher is expected to identify the sample to be investigated, determine the appropriate sample size depending on the study, and decide whether to run a randomized or an observational experiment.

Consequently, this leads to a successful yield of an extreme value of the quadratic function. Besides linear programming, it is a significant step to solve elaborate problems involved in economic models and other non-linear programming problems. It is also applicable in solving several problems that are of best interests to itself.

On visiting the lottery number normally, present 38 with corresponding 142 events during the least commonly occurring number is 20 with 90 events. The question thus pertains to how the prevailing information is capable of affecting an individual’s choice of the lottery number next time they purchase the ticket. 

The Hex theorem is intuitive, but it requires invoking complicated topological results to prove it. John Nash proved hex theorem, but he never published his proof (Weinberger pp. 380). David Gale provided a simple graphical explanation of the theorem showing equivalence between Brouwer Fixed Point Theorem and Hex Theorem.

Already in the 18th century, the potential of using games as a pedagogical tool was already brought to the fore and, in the 1920’s at least in the US there was an attempt to systematically incorporate games in school curricula. However, it was only during the 1950s and 1960’s that games began to be part of the school systems.  

Pell numbers arise in olden times and most remarkably in rational approximation to solving the square root of 2. If two integers, that is x and y form an answer to a Pell equation. The denominator for every fraction is a Pell number; the numerator is the addition of a Pell number and its antecedent in the Pell numbers series.

A residual plot that seems to trend upwards or downwards such as this is almost certainly symptomatic of a poor ambiguity fix and should be investigated and corrected. Corrective action may be to raise the elevation mask, eliminate some satellites, change the start and/or finish times, or as a last resort remeasure the observation.

The answers using equations are the same as 7.24 or -1.25 using quadratic formulae while the Newton method gives an answer -1.24. Then f is the set of all ordered couples of the form⟨x,x^2+ 2⟩, for x a real number. On the other hand, for any particular real number x, f(x) is simply the real number x2 + 2. 

It is equally important to note that the value S squared represents the characteristic equation of this differential equation. After getting the above equation, we go a step further and divide the equation on the left-hand side with that on the right-hand side, therefore making Y the subject of the resulting equation.

It is possible to conceive that the volatility that is ascertained by using the statistics will be more accurate than the small determined from data given the larger frequencies of statistics for every day. Although in some respects such results point at the success of ascertaining simple volatility estimation from high-frequency statistics.

The function enables the calculation of larger amounts of options at fast speeds which is good for investors with a large amount of data, therefore, utilizes this model extensively. However, the model’s approach of calculating options at their expiration makes it weaker than the Binomial model whose calculations are done on several internals.

Some of the tradeoffs include laying off of excess workers which may result in unemployment hence leading to the reduction in the workforce. The trade-off can lead to employing a more sophisticated technology which may result in additional expenses to the firm. Increased cost means a reduction of the profits hence the benefit for the short run.

The basic requirement is that for a sample in size n, all possible samples of the size must have an equal chance of being selected from the population. In producing randomness numbers various methods are used however some produce errors which make the data samples and unrepresentative of the population.