Maths EE Topic Ideas + Examples

You still haven't decided on the topic of your Maths EE? You can write on any topic that has a mathematical focus. Check out this list of 15 propositions and examples of extended essays, to see the variety of topics that you can investigate. 

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Cryptography

Differential equations

Engineering

Mathematical modeling

Optimization & applied calculus

Math EE Ideas

1. Usage of elliptic curves in cryptography: The right to privacy is crucial in online communication due to the prevalent risks of digital security breaches. Major companies like Meta and Google employ cryptography to store and transmit personal information securely. This EE examines how modern cryptography (including algorithms like RSA and elliptic curve cryptography) utilizes mathematical principles to safeguard information transmitted over the internet, addressing the growing concerns about digital security and privacy.
   
    

2. The application of Laplace Transformation on differential equations: This essay delves into the application of engineering mathematics, particularly Laplace Transformation (LT), in solving complex equations relevant to undergraduate engineering students - related to undamped vibration and Kirchhoff's laws of current and voltage. It emphasizes the importance of LT as a widely used method in mathematics and physics, providing clear illustrations to aid comprehension. The essay focuses on how LT can effectively solve complex linear differential equations, including those related to Kirchhoff's laws, digital signal processing, and system modeling. Additionally, it explores the accuracy of LT through experiments, particularly in addressing second-order differential equations common in physics applications. 
   
    

3. Exploring Consonance and Dissonance through the Fourier Series: This study explores the relationship between music theory and mathematical descriptions of stringed instruments. It investigates how strings' vibrations produce consonant and dissonant sounds by analyzing the wave equation and its solutions. By employing a variable separation approach and establishing the uniqueness of the solution, the study aims to understand the formation of these sounds. The research question guiding this inquiry is: "To what extent do mathematical descriptions of string motions within stringed instruments, described by the Fourier Series, provide insight into the concepts of consonance and dissonance in music theory?"
   
    

4. Lotka-Volterra model: The Extended Essay investigates the predator-prey relationship at Isle Royale National Park, USA, and Leigh National Park. Linearization of the Lotka-Volterra model is necessary for analysis, involving concepts like the Jacobian matrix and Eigenvalues. Graphical representations support the application of the model in understanding predator-prey dynamics, leading to the research question: "To what extent does the Lotka-Volterra model aid in comprehending predator-prey relationships in ecosystems?"
   
    

5. Pell's equation in cryptography: Cryptography ensures secure communication between sender and receiver, commonly used in text messages and financial transactions, employing encryption methods like RSA. However, RSA encryption is susceptible to low exponent attacks, posing risks to privacy and authenticity, particularly for entities like government and military. The paper delves into RSA operation, addressing security challenges and efficiency, followed by an exploration of Pell's equation and its role in prime fake modulus implementation.
   
    

6. Matrix analysis of Game theory used to guide foreign policy: Game theory simplifies interactions into mathematical models to predict outcomes beneficial for players. It assumes rational decision-making, full information, and predetermined payoffs, although these assumptions may not reflect real-world scenarios accurately. US-Iran tensions, characterized by complex interactions, offer an opportunity for game theory analysis to guide foreign policy decisions, considering the array of strategies available to each party.
   
    

7. Optimizing a suspension bridge: Suspension bridges are popular for long distances due to their efficiency and cost-effectiveness. Investigating optimal bridge designs for industrial transportation routes. The bridge's structure typically consists of two identical sides connected by main cables shaped like a catenary, with vertical towers evenly spaced along the length. The research question focuses on determining the height and number of towers required for the bridge to bear heavy loads at minimal cost. 

   
    

   
    

8. Application of trigonometry in astronomy: Trigonometry finds extensive applications in various fields including astronomy, navigation, and construction. Its concepts involve the study of angles and distances within triangular shapes, aiding in calculations related to real-life scenarios. Astronomy, on the other hand, is the scientific study of the universe and heavenly bodies, providing insights into celestial phenomena and aiding in timekeeping during ancient times. Despite being distinct fields, trigonometry and astronomy are intertwined, with trigonometric principles being applied in astronomical calculations to understand celestial motions and distances. This paper explores the astronomical applications of this branch of mathematics. 
   
    

9. The Analysis of Approaches and Extension of a Combinatorial Geometry Problem: In this essay, the author aims to analyze, solve, and expand upon a challenging problem from the 2017 International Mathematical Olympiad (IMO), which involves a hunter and an invisible rabbit playing a game in the Euclidean plane. Despite its seemingly simple setup, the problem is statistically the most difficult in IMO history, with only two out of 615 contestants solving it correctly within the allotted time. The problem requires a combination of mathematical areas such as geometry, optimization, and proof formation. The author's interest in understanding how so few people managed to solve the problem motivates them to attempt a solution, compare their approach with successful participants, and explore real-world applications of the problem.
   
    

10. Application of mathematical concepts in forensic science: Forensic science involves analyzing evidence from crime scenes to aid investigations and prosecutions. This essay focuses on two branches: blood spatter analysis and estimating the time of death. Trigonometry is used in blood spatter analysis to determine angles of impact, while calculus and Newton's laws are employed to estimate the time of death based on temperature loss. The research question explores the extent to which trigonometry, elliptical geometry, and calculus assist forensic analysts in these areas, highlighting the practical applications of mathematics in real-life scenarios.
    
     

11. Analysis of the distribution of cards: The egg game, chosen for this investigation, is a game of chance where players receive cards with symbols, numbers, or names, aiming to collect four identical cards to win. Despite being widely known in some countries, it lacks a thorough analysis of online resources. Its unique rules make it an interesting subject for applying concepts of combinatorics and probability. The research question focuses on determining the probability distribution of outcomes based on the number of identical cards received by each player in the egg game with three players.
    
     

12. Application of modular arithmetic in the field of number theory:  This paper aims to explore modular arithmetic and its applications in number theory. It discusses significant theorems essential to the topic and presents original solutions to number theory problems, primarily from the UK Mathematics Trust. Overall, the essay highlights the significance and practicality of modular arithmetic in pure mathematics, cryptography, and checksum calculations, providing elegant solutions to mathematical problems.
    
     

13. Links between the prime numbers and the Riemann Zeta Function: The essay delves into the Riemann Zeta Function, a mathematical concept defined for the complex plane. It explains how the function converges for certain values of its argument and diverges for others, particularly focusing on its behavior at s=1. The essay discusses the Riemann hypothesis, a conjecture proposed by Riemann regarding the function's zeros, which remains unsolved to this day and is considered one of the most important challenges in mathematics. Furthermore, it investigates the connections between the Riemann Zeta Function and prime numbers, aiming to shed light on the mysteries surrounding both concepts.
    
     

14. Optimization of scoring points in rugby union: The study investigates the optimal distance from the try line to position the ball for a conversion kick in rugby union using mathematics. It acknowledges the intuitive approach of kickers but proposes that mathematical analysis could improve success rates. The personal motivation behind the investigation stems from the author's interest in both rugby and mathematics, aiming to contribute a useful solution to a real-life problem while advancing knowledge in both areas.
    
     

15. The RSA algorithm and its vulnerabilities: This extended essay aims to explore the mathematical background of the RSA algorithm, a widely used encryption method, and analyze its workings and vulnerabilities. The investigation seeks to determine the extent to which the RSA algorithm can provide secure encryption despite its known weaknesses.