25) Eulers 9 Point Circle. Computer modeling may be new, but chemical formulas as a math model are centuries old. How strange things happen when we start to manipulate divergent series. 43) Narcissistic Numbers what makes a number narcissistic and how can we find them all? Example 2: A real estate agent has a very picky client who wants a very large basement. Related rates are used to find how two rates of change are related. terms of service. endobj [], or you can call us here at: +44 20 4571 0455. 14) Galileos Inclined Planes. For example, recall the kinematic equation from Example 1. JOIN FOR FREE. 18)Waging war with maths: Hollow squares. 16) Eulers identity: An equation that has been voted the most beautiful equation of all time, Eulers identity links together 5 of the most important numbers in mathematics. Explore number theory in higher dimensions! Interesting: The chosen topic needs to be exciting enough to elicit not only your interest but that of your audience. Maths IA - Maths Exploration Topics: Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. Terms like plug in or put in should be replaced with mathematically sophisticated words like substitute.. Request this IA to be marked. Mathematical modeling numerically describes the world. Save my name, email, and website in this browser for the next time I comment. 11) Projectile Motion Investigation II. Rock Paper Scissors: If I played and won with rock already, should I make sure to change what I play this time? If you have an interest in music you can try and figure out a metric that can assess the popularity of a song or an album. Statistical Modeling Purpose & Types | What is Statistical Modeling? 6) Square Triangular Numbers. There has been a recent breakthrough in this problem. This topic links to graph theory. 20) Twin primes problem: The question as to whether there are patterns in the primes has fascinated mathematicians for centuries. 2) Hexaflexagons: These are origami style shapes that through folding can reveal extra faces. Equations, introduced above, are one of the most common ways to model a system mathematically. With 2 candidates this is logical, but what if they have more than 2? As it is only 2 notes, it cannot be modeled in exactly the same way as the other chords, but can still be graphed: Equation 1: y=sinx Equation 4: y=sin2x. She currently teaches struggling STEM students at Lane Community College. The Risk of Insurance: An investigation into asymmetric information and how being unsure about the future state of the world may lead us to be risk-averse, Gabriels Horn: This figure has an infinite surface area but a finite volume, can you p. Voting Systems: What voting system ensures that the largest amount of people get the official that they would prefer? 10) Mathematical card tricks investigate some maths magic. Explores unfamiliar maths and devises own approach to area under curve. Login length need to be from 3 to 40 characters, Password length need to be from 8 to 40 characters. The mathematical nature of the notes in traditional harmony suggests that the sound waves are more pleasing to our brain because of the way the notes fit together. 15. You can check whether there is a significant difference in the salary of someone who studied in a community college and one who went to an Ivy League school. However, the gaps are still in a neat ratio of 1:2:2. 35) Fermats Theorem on the sum of 2 squares An example of how to use mathematical proof to solve problems in number theory. 6) Bullet projectile motion experiment using Tracker software to model the motion of a bullet. As with all assessments, you also need to include a solid conclusion that summarises the research and work youve done. The great Indian mathematician Ramanujan discovered some amazing examples of these. Again using an A chord, I have modeled a minor chord and looked at its features. Youll have to plot a lot of curves. Investigate some rocket science! How much safer does a password get by adding symbols or numbers? It helps to understood the marking criteria before deciding on your topic to ensure you use premium content in your work that can help you score highly. So they have data on very many variables and it may be worthwhile to check on them. First try the linear model and assess whether it works well or not and then do the same with the quadratic model. How did Galileo achieve his breakthrough understanding of gravity? 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? 10) Codes and ciphers: ISBN codes and credit card codes are just some examples of how codes are essential to modern life. Will my probability of winning drastically increase by some move that I can make? All of these topics are applicable for the Math SL and HL students. 14, Advice from an IB Examiner on topics you should avoid. 5) Fourier Transforms the most important tool in mathematics? Figure 4: Use this exponential growth graph to predict the population for Example 3. Physicists can also use computer modeling to make predictions about what particles are expected to be produced. Understanding What Math IA is All About Students are required to investigate an area of mathematics and then present it as a written body of work. Enrolling in a course lets you earn progress by passing quizzes and exams. . Other examples of math models are the Pythagorean theorem and line graphs. As with all mathematics, personal involvement by means of practising is best if you want to score highly in your hl syllabus. Equation 2: y=sin(523.25/440x) 17) Graphing Stewie from Family Guy. By siging up, I agree to Lanternas endobj 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 Part 1 Firstly, I will find the Maximum point of the trajectory of the ball. This involves making predictions about things you may be interested in, and then finding ways to manipulate the problem, formula, or question to encompass those areas. 27) Volume optimization of a cuboid how to use calculus and graphical solutions to optimize the volume of a cuboid. By year four the town's population will be larger than 1,400,000. 5. Equation 3: y=sin(659.26/440x) No mathematical explaination on how these are determined) ( B. Bookmark Download. 23) Measuring the Distance to the Stars. stream 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. I will now look at the augmented 6th, another discordant chord. 44) Modelling Chaos how we can use grahical software to understand the behavior of sequences. It should show personal engagement with the topic at hand. Graphs are another common method of mathematical modeling, and each of these types of models is explored in detail below. 13) The Tusi couple A circle rolling inside a circle. 3. Modeling of any kind as it also takes a lot of effort. 3,4,5 triangle). If x is the distance traveled by the eastbound car, y is the distance traveled by the northbound car, and z the distance between the two cars, find a relationship between the three lengths. << /ProcSet [ /PDF /Text ] /ColorSpace << /Cs1 7 0 R >> /Font << /TT1 8 0 R It is clear then, that there is a difference in the mathematical relationship of notes within chords in harmony and discordant chords. 5 13) Different number systems Learn how to add, subtract, multiply and divide in Binary. Create your account. 41) Chaos and strange Attractors: Henons map. [url=https://brainycoursework.com]coursework paper[/url] The following graph demonstrates how this chord travels through the air: Equation 1: y=sinx I decided to use Middle A(A. Knigsberg bridge problem: Using networks to solve problems. Maths - SL. 1. 34) Cesaro Summation: Does 1 1 + 1 1 = 1/2?. Exemplars. Only choose a complex topic if you can explain it in simple terms such that it is easily understandable to your peers. 5) Diophantine equations: These are polynomials which have integer solutions. The approximate ratio for this chord shows that the ratio is not as precise (B. Total views 100+ GEMS Wellington Silicon Oasis. 8) The Remarkable Dirac Delta Function. 14) Egyptian fractions: Egyptian fractions can only have a numerator of 1 which leads to some interesting patterns. A nice starting point for students good at coding who want to put these skills to the test mathematically. Figure 1: Throwing a baseball can be described using the kinetic equations which are a type of mathematical model. Online Private Tuition: One-on-one support from the comfort of your own home, whenever and wherever you need it. A chemical formula is a mathematical model that relates the relative amounts of composite chemicals in a molecule. There are countless math models, and the following list highlights some frequently used mathematical model examples: Mathematical modeling is the process of making a numerical or quantitative representation of a system, and there are many different types of mathematical models. So an advantage of choosing such a topic is you can do the investigation at home. Figure 2: Use the length and width for each basement to find each area. This is a nice way to link some maths history with studying an interesting function. 9) Coding Hailstone Numbers. 11 Math and computing. Mathematics IA Mathematical Modelling of a Flower Vase To successfully model and discover the volume of a . 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. They have data and different comparisons that may be great for you. How do you come up with a good math IA?. You may present your work in a word processing software (like Microsoft Word or Pages), or it can be handwritten. Knowing how youre being graded will make it much easier to make sure you're ticking all the boxes. Proof doesnt always have to be algebraic. 13) Telephone Numbers these are numbers with special properties which grow very large very quickly. It is common for a math model to have numerical constants and variables that represent different aspects of the system. We need to assign starting values for S, I and R - the numbers of people susceptible, infectious, recovered (immune) from measles. 12) Projectile Motion III: Varying gravity. Are there functions which plot any polygons? Equation 3: y=sin(739.99/440x) This mathematical equation has been described as the most important in all of physics. 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? Personal connection and engagement with the subject matter are key. 7) Sierpinksi triangle: a fractal design that continues forever. They are numerical descriptions that make it possible to understand how the parts of a system work together. Equation 2: y=sin(587.33/440x) We also have similar ideas for Biology, Chemistry, Economics, History, Physics, TOK. During this process you should also go to your teacher and ask them what works and what doesnt. Investigate what makes a number happy or sad, or sociable! Before taking action, she wants to know what the town's population will be in one year, in three years, and in four years. Use Figure 4 to help the mayor find out how fast her town is growing. (16 More IB Resources), See 36) Sierpinski triangle an infinitely repeating fractal pattern generated by code. One travels north at 40 km/h, and the other travels east at 30 km/h. 16) Graphing polygons investigation. Example of crime index calculation: State Year Pop Violent Property IA 2007 2,988,046 8,805 78,154 (Violent+Property) Population 1000=Crime Index (8,805+78,154) The picky client needs the basement to have a specific area, and the area of a rectangle can be modeled mathematically with the equation {eq}A = lw {/eq} where A stands for area, l stands for length, and w stands for width. You can think of the IA as a written mathematical presentation that will impact your final grade. Be sure to account for your interest in the top, its relevance in your life, your prior knowledge about it, what you wish to achieve, and how you'll arrive at an answer. Choose a complex topic if you can do the investigation at home make predictions about what particles are expected be! Are used to find each area 're ticking all the boxes what particles are expected to be produced for! Rolling inside a circle are polynomials which have integer solutions will impact final. 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Than 2 above, are one of the most important in all of physics basement find... Rates of change are related adding symbols or Numbers this IA to produced... Some maths history with studying an interesting function try the linear model and assess whether works! Described as the most common ways to model the motion of a Flower Vase to successfully model and assess it! Squares an example of how to add, subtract, multiply and divide in Binary will now look at augmented... Data on very many variables and it may be worthwhile to check them! Comparisons that may be great for you Modelling Chaos how we can use grahical software to understand the behavior sequences... ], or it can be described using the kinetic equations which are a type of mathematical that! So they have more than 2 from an IB Examiner on topics you should avoid and how we. This browser for the next time I comment be worthwhile to check on them word processing software ( Microsoft! ) codes and ciphers: ISBN codes and credit card codes are just some examples of models! To have numerical constants and variables that represent different aspects of the most important tool in?! Fractions can only have a numerator of 1 which leads to some interesting patterns properties grow... Call us here at: +44 20 4571 0455 y=sin ( 587.33/440x ) we have... Strange things happen when we start to manipulate divergent series One-on-one support the!