# 45 Interesting Mathematics Research Project (Paper) Topics and Ideas

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Mathematics Research Project (Paper) Topics and Ideas
Mathematics includes the study of such topics as quantity, structure, space, and change. It has no generally accepted definition. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of conjectures by mathematical proof. We have developed a list of interesting mathematics research project (paper) topics as follows:
1. Evaluating the Validity of Perron’s Paradox
Discuss: Perron’s paradox, highlights the danger of considering a solution to a mathematical problem if the solution is actually nonexistent.For example, if we assume the largest natural number exists and it is N,
Therefore if
N>1,
then
N^2>N,
and this contradicts our hypothesis that N is the largest natural number, hence the largest natural number is
N=1,
and this would seem to be absurd, hence it emphasizes the danger of assuming a solution exists while it is actually nonexistent.
Let’s reexamine this again.
2. Evaluating the Validity of Video Education for Mathematical Studies: Case Study of videos of mathematical concepts made by students
Discuss: This study presents a research scenario of a teaching experience in which students use ICT to develop video tutorials of the mathematical concepts from the Mathematics for Business Studies and evaluates the effectiveness of the process on their understanding of the subject matter.
3. A Critical Analysis of the Henstock Integral and Riemann Integral
Discuss: The Riemann integral, which is familiar to the reader from calculus, can be loosely defined as the limit of the sum of narrow “strips” of the area under a function taken as the width of each strip goes to 0. This Study will apply the Henstock-Kurzweil integrals to deal with linear differential equations.
4. What is Musical Mathematics? Evaluating the Music Composers who have used Mathematical Formulae in Their Compositions
Discuss: Many Music composers have used mathematical formulas in their compositions. This study will evaluate the best in history and develop a mathematically perfect tune for a specific audience.
5. Examining the Relationship between Horizontal/Vertical asymptote of reciprocal functions and exponential function.
Discuss: Using the Maclaurin power expansion, for
a=m2−n2, b=2mn, c=m2+n2 where m>n>0
for any 2 values of m and n the above formula will give a Pythagorean Triple.
To get a Primitive Pythagorean triple, m and n have to co-prime and not both odd.
This Study will Seek to understand this formula
33. Developing 3D Mapping System: Understanding the points required to map a 3D shape
Discuss: A shape is fixed by three points in 3D. In terms of translations and rotations, you can think of it this way. If point A maps to A’, that takes care of three translations, but the shape can freely rotate attached to A’. If a second point B maps to B’, the shape can only rotate around line A’B’. A third point C’ fixates that last degree of freedom.
34. Gender Roles in Instrumentation in Mathematics Education
Discuss: Contrary to the common perception that mathematics is a pure mental activity, the importance of tools in mathematical activity has been largely acknowledged: Ç many of the actions of doing mathematics involve selecting, using and creating tools.
35. Understanding Image Processing and Fourier Wavelet Methods
Discuss: Image processing based on the continuous or discrete image transforms are classic techniques. The image transforms are widely used in image filtering, data description, etc.
36. A Comparative Analysis of Flipped Classroom and Traditional Classroom in a Given School
Discuss: This study aims to determine the perception of the lecturers’/students’ and their achievement between two learning cultures, the traditional classroom and flipped classroom in a Given School.
37. Solving Inverse of Large Matrix: Utilizing Arnoldi Method to Solve Quadratic Eigenvalue Problems
Discuss: First a large size matrix requires sufficient memory to inverse the matrix. Secondly, there are several mathematical techniques available to solve the inverse of a matrix.
38. Children are the Building Blocks of Economic Complexity: The Economic Complexity Index Formula
Discuss: This Study examines the question of economic complexity is equivalent to asking whether we can infer properties such as the diversity and exclusivity of the Lego pieces inside a child’s bucket by looking only at the models of a group of children.
39. Formation, Coordination, Development and Adaptation of Small Groups of Complex Systems
Discuss: A conceptually elegant analysis of groups as systems. Although the systems approach has been growing more influential in various fields of social psychology in the last ten years, no one has put forward a definitive analysis that applies with fidelity the general systems approach to group processes.
40. A Critical Review of Quantum Evolutionary Algorithm: Analysing Invasive Weed Optimization
Discuss: This Study will analyse a new optimization algorithm based on developing the invasive weed optimization algorithm by quantum computing.
41. Developing a Detection Algorithm for Melanoma using a Hybrid Neural Network
Discuss: Melanoma is among the most dangerous forms of cancers. Early detection is the best defense against melanoma. This Study will analyse a new efficient method for detecting melanoma via images.
42. Meta-Heuristics Algorithm and Global Solution: Sampling Distribution for the Probability of Finding a Global Max/Min Levels
Discuss: Meta-heuristics are the most recent development in approximate search methods for solving complex optimization problems that arise in business, commerce, engineering, industry, and many other areas.
43. Validating the impact of Doppler Shift on the rate of information transmission?
Discuss: When a modulated signal lasting atime =Tis subjected to an optical Doppler shiftK (K=shifted frequency/original frequency)the Doppler-shifted signal will lastT/K.This because all shifted harmonics of its Fourier series with a (fundamental period of T) will last1/K timesthe period of the original harmonic.
44. A Critical Review of Mathematics Anxiety: Why Primary School Studies are afraid of Mathematics
Discuss: Thousands of studies have been published that touch on the topic of “math anxiety.” The overwhelming fear of math, regardless of one’s actual aptitude, affects students of all ages, from kindergarten to grad school. This study will analyze the reasons for this and best teaching practices to reduce it.
45. Understanding Monte Carlo Methods (Industrial Mathematics)
Discuss: Monte Carlo simulations are used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables. It is a technique used to understand the impact of risk and uncertainty in prediction and forecasting models.
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