44) Modelling Chaos how we can use grahical software to understand the behavior of sequences. Furthermore the musical chords are representated with the help of multiple sinosodial curves, so that they can be broken down and their mathematical relation can be understood. The kinematic equations can be used to describe the motion of any moving object, and because they relate different quantities present in a single system to describe another aspect of the system, the kinematic equations are considered a mathematical model. Are you getting ready to present your Math IA? oZWE|-jT (XA IA. I altered the wavelengths, or frequencies, of the graphs by changing the coefficient of x. This investigation was very limited, as I was not able to research properly how electronic instruments work, and how they differ from mechanical instruments. I wanted to make the sound wave of this note equal to the sine wave, which meant making 220Hz equivalent to ( typing error). However, there is not necessarily a difference in chords that are in harmony and discordant chords. Maths can be used to both make these codes and break them. We've trained a system that solves grade school math problems with nearly twice the accuracy of a fine-tuned GPT-3 model. Share. Equation 1: y=sinx Example 1: Use the kinematic equation {eq}v_f = v_i + at {/eq} where {eq}v_f {/eq} means final velocity, {eq}v_i {/eq} means initial velocity, a stands for acceleration, and t stands for time to answer the following question: A race car driver sits at the starting line. These waves look very similar to the major chord waves, as only one note has changed; the C# has gone down by a semitone. Why does the twin paradox work? These are some of the best Math IA Topics. 33) The Chinese Remainder Theorem: This is a method developed by a Chinese mathematician Sun Zi over 1500 years ago to solve a numerical puzzle. This is a puzzle that was posed over 1500 years ago by a Chinese mathematician. It could be something that interests you and you will like to know the mathematics behind it. Find out! Save my name, email, and website in this browser for the next time I comment. Knigsberg bridge problem: Using networks to solve problems. How can we use computers to gain a deeper understanding of sequences? 7) Patterns in Pascals triangle: There are a large number of patterns to discover including the Fibonacci sequence. 6) Handshake problem: With n people in a room, how many handshakes are required so that everyone shakes hands with everyone else? Mathematical modeling is used by scientists, mathematicians, businessmen, and economists. Years are on the horizontal axis and population is on the vertical axis. Coverage: Calculation of rate of deforestation, and afforestation. 11 Mathematics and Physics. The three main types of mathematical models are equations, graphs, and computer modeling, and each of these can be used to learn about different aspects of a system. At what rate is the distance between the cars increasing two hours later? However, this is just a theory and would have to be tested more thoroughly. The IB is all about learning, so be sure to show the marker your growth throughout the IA. How can we find the area of any polygon? [url=https://brainycoursework.com]coursework paper[/url] Choose your own pattern investigation for the exploration. You should do some research before you embark on this Math IA Idea and learn everything you need to know. This equation stated how initial velocity, acceleration, and time could be used to find final velocity, and, in Example 1, this numerical statement was able to give a quantitate description of how fast the race car and driver were traveling. So in this method you are testing the difference between two means and you are checking whether there is a significant difference. The mathematical model definition is that a mathematical model is a quantitative description of a system. For example, it is possible to describe how a baseball travels through the air after it has been thrown using the kinematic equations from physics. Can we use a mixture of pure maths and computing to solve this problem? Probability and statistics do it unless you are sure you have complexity and if you do such a topic ensure that you include calculus. Ib Math Studies Ia Thesis Example When somebody should go to the ebook stores, search initiation by shop, shelf by shelf, it is truly problematic. She currently teaches struggling STEM students at Lane Community College. Login length need to be from 3 to 40 characters, Password length need to be from 8 to 40 characters. For example, to find how fast the distance between two cars increases, if we know the speeds of two cars that travel away from a 90-degree intersection, we will use the related rates model. The intervals are known as a perfect fourth and perfect fifth are, as the name suggests, considered to be the most harmonic intervals. Modelling the population of Singapore. However, redoing them would not be such a bad idea as long as you ensure that you infuse some complexity, personal involvement and more critical thinking. Give us the email address you use to log in to Lanterna and well send you instructions for resetting your password. Importantly, make sure to also discuss some of the challenges in your IA and what you would/could explore with more time and more words. Limited understanding of notes played together), Equation 1: y=sinx Its a really useful tool that allows you to compare different variables. G,m m0Z-d_u`aVO*']SFgC\xzzCDlr.2"} V#JTwDNty^~(Tbt.V90n _*}HD]fu-U\75bJ;L.k|>MUYgog3K 35) Sphere packing how to fit spheres into a package to minimize waste. 2. It should display a degree of creativity in that you present mathematical ideas in your own way and explore the topic from various different perspectives. The Stable Marriage Problem: Is there a matching algorithm that ensures each person in society ends up with their one true love? 9) Optimization of area an investigation. This is a function which is used in Quantum mechanics it describes a peak of zero width but with area 1. Mathematical modeling numerically describes the world. endstream The Pythagorean theorem states that the square of the hypotenuse in a right triangle equals the sum of the squares of the legs. The evidence here suggests that notes in harmony fit into a mathematical context, whereas discordant notes do not. Erroneous notation, it should be 554.37x/440). This chord is also known as The Devils Chord, as it is considered to be the most the unpleasant sounding chord in music. It involves understanding the modulo operation. We look forward to joining the Lanterna and being part of your success. So there we have it: 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! Look out for these during the Winter and Easter breaks before the final exam. Analysing Data: In the 200 meter dash, is there an advantage to a particular lane in track? It solves about 90% as many problems as real kids: a small sample of 9-12 year olds scored 60% on a test from our dataset, while our system scored 55% on those same problems. 1) Modular arithmetic This technique is used throughout Number Theory. Equation 2: y=sin(523.27/440x) 13) Graphically understanding complex roots have you ever wondered what the complex root of a quadratic actually means graphically? By submitting this form, I agree to the data entered being used by Nail IBNSW for sending 39) Zenos Paradox Achilles and the Tortoise A look at the classic paradox from ancient Greece the philosopher proved a runner could never catch a tortoise no matter how fast he ran. To model this problem, we need the following tools. Optimization Problems Steps & Examples | What is Optimization in Calculus? Instead of comparing means, youll be comparing proportions. Stacking Balls: Suppose you want to place balls in a cardboard box, what is the optimal way to do this to use your space most effectively? Look at the inherent probabilistic nature of the universe with some quantum mechanics. Here is a geometric proof. Gini coefficient: Can you use integration to derive the gini coefficient for a few countries, allowing you to accurately compare their levels of economic inequality? %PDF-1.3 Follow in the footsteps of a genius! 39) Finding the average distance between 2 points on a hypercube. . Whatever you choose, remember that you will create a new exploration of complex ideas. Then you found out the difference between the proportions of three point shots vs two point shorts. I started by working out how to model a single note. Examples of Mathematical Modeling Tales from the Crypt Matthew D. Johnston,1,3,*Carina M. Edwards,1,3,Walter F. Bodmer,2Philip K. Maini,1,4and S. Jonathan Chapman3 Matthew D. Johnston 1Centre for Mathematical Biology; Mathematical Institute; University of Oxford; Oxford, UK The great Indian mathematician Ramanujan discovered some amazing examples of these. 5) Diophantine equations: These are polynomials which have integer solutions. So for instance you decided to correlate 2 things. An interesting topic can also stem from liking a particular topic of subject in math such as calculus and then you can find something in relation to even Formula 1 or a real life situation that involves calculus. A model in math can be different depending on the type of model or what the model is describing, and some of the uses of mathematical models are: An error occurred trying to load this video. Copyright 2023 Get the grade you deserve. xU]hU>3;yCmK+u!aR&MM6Ut'3 } 18. To calculate the car and driver's final speed, all that is left to find is their initial speed, and since the car and driver begin at rest, {eq}v_i = 0 {/eq} m/s. % October 29, 2021. Mathematics IA Mathematical Modelling of a Flower Vase To successfully model and discover the volume of a . Minor chords are also considered to be in harmony. This is an nice example of how you can investigation optimization of the area of different polygons. How strange things happen when we start to manipulate divergent series. Looking at Figure 3, the population starts out at a little over 100,000 people, and it does not grow much the first year. Equation 3: y=sin(739.99/440x) This graph looks very similar to the major graph, but the actual values, shown in the The following table, are slightly different. 5 It is essential that you select the appropriate topic for you that aligns with your interests and you dont pick a topic just because very many people have done it. It is also worth noting that the maths produced should be at a similar level to the math you cover in your syllabus. 31) Grahams Number a number so big that thinking about it could literally collapse your brain into a black hole. Pythagorean Theorem Diagram & Model | Why is the Pythagorean Theorem Important? Can we use a mixture of pure maths and computing to solve this problem? 50) Square triangular numbers. endobj This may indicate the start of a pattern. Figure 1: Throwing a baseball can be described using the kinetic equations which are a type of mathematical model. The ratios of frequencies of chords in harmony are more concise. Using x'(t)=30, y'(t)=40 and the distance of each car after two hours, we obtain: 4. Your data shall be kept until you unsubscribe. The IB needs us to do more than just show what weve done. 9) Designing bridges Mathematics is essential for engineers such as bridge builders investigate how to design structures that carry weight without collapse. Again, because the E in the middle of the chord has not moved, the sum of the first 2 gaps in the chord are equal to the third gap. 11) Understanding the fourth dimension: How we can use mathematics to imagine (and test for) extra dimensions. 5) Project Euler: Coding to Solve Maths Problems. Putting it all together gives: {eq}v_f = v_i + at {/eq} -> {eq}v_f = 0 + 80*10 {/eq}. The body of your IA exploration should focus on the particular topic you have chosen to investigate and the relevant mathematical material that will address the intended aim of the work. IA. IA Review. Fermats Last Theorem is one of the most famous such equations. For this reason, this theory does not only apply to sound coming to electronic instruments but every kind of instrument. 1) The Van Eck Sequence The Van Eck Sequence is a sequence that we still dont fully understand we can use programing to help! There are two fundamental questions that you can ask yourself at the beginning of this process. Find out how! Youd be better off carefully thinking about what youre going to do and what interests you, and what would make you have the most personal engagement and the ease of access to data that you need. May 2022. The poor mayor does indeed have a problem! Pages 15. 6) Batman and Superman maths how to use Wolfram Alpha to plot graphs of the Batman and Superman logo. 15) Julia Sets and Mandelbrot Sets We can use complex numbers to create beautiful patterns of infinitely repeating fractals.