Category: International Maths Olympiad

Using the tools of computational complexity, researchers have discovered it is impossible to figure out whether certain Super Mario Bros levels can be beaten without playing them, even if you use the world’s most powerful supercomputer.

Figuring out whether certain levels in the Super Mario Bros series of video games can be completed before you play them is mathematically impossible, even if you had several years and the world’s most powerful supercomputer to hand, researchers have found.

“We don’t know how to prove that a game is fun, we don’t know what that means mathematically, but we can prove that it’s hard and that maybe gives some insight into why it’s fun,” says Erik Demaine at the Massachusetts Institute of Technology. “I like to think of hard as a proxy for fun.”

To prove this, Demaine and his colleagues use tools from the field of computational complexity – the study of how difficult and time-consuming various problems are to solve algorithmically. They have previously proven that figuring out whether it is possible to complete certain levels in Mario games is a task that belongs to a group of problems known as NP-hard, where the complexity grows exponentially. This category is extremely difficult to compute for all but the smallest problems.

Now, Demaine and his team have gone one step further by showing that, for certain levels in Super Mario games, answering this question is not only hard, but impossible. This is the case for several titles in the series, including New Super Mario Bros and Super Mario Maker. “You can’t get any harder than this,” he says. “Can you get to the finish? There is no algorithm that can answer that question in a finite amount of time.”

While it may seem counterintuitive, problems in this undecidable category, known as RE-complete, simply cannot be solved by a computer, no matter how powerful, no matter how long you let it work.

Demaine concedes that a small amount of trickery was needed to make Mario levels fit this category. Firstly, the research looks at custom-made levels that allowed the team to place hundreds or thousands of enemies on a single spot. To do this they had to remove the limits placed by the game publishers on the number of enemies that can be present in a level.

They were then able to use the placement of enemies within the level to create an abstract mathematical tool called a counter machine, essentially creating a functional computer within the game.

That trick allowed the team to invoke another conundrum known as the halting problem, which says that, in general, there is no way to determine if a given computer program will ever terminate, or simply run forever, other than running it and seeing what happens.

These layers of mathematical concepts finally allowed the team to prove that no analysis of the game level can say for sure whether or not it can ever be completed. “The idea is that you’ll be able to solve this Mario level only if this particular computation will terminate, and we know that there’s no way to determine that, and so there’s no way to determine whether you can solve the level,” says Demaine.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Matthew Sparkes*

Feedback plays a vital role in mathematics education, guiding students toward deeper understanding and fostering a supportive learning environment. This article delves into the importance of specific and actionable feedback in mathematics education and explores strategies for both giving and receiving feedback effectively.

Understanding Feedback:

In mathematics education, feedback transcends mere praise or criticism—it is a nuanced tool for academic growth. Effective feedback should be clear, and concise, and provide guidance for improvement. It should highlight students’ strengths, address any misunderstandings, and offer actionable steps for progress.

Key Components of Effective Feedback:

Specificity: Feedback should pinpoint areas for improvement and clarify the path to success. Students need to know precisely what they need to do to enhance their understanding.

Actionability: Feedback should be actionable, outlining steps for students to move forward. This empowers students to take ownership of their learning journey.

Importance of Feedback:

Feedback serves multiple critical purposes in mathematics education:

Promoting Learning: It catalyzes academic growth by guiding students towards deeper understanding and mastery.

Building Motivation: Constructive feedback inspires students to strive for excellence and fosters a growth mindset.

Fostering Relationships: Feedback provides an opportunity for educators to connect with students on a deeper level, building trust and rapport.

The Human Element: Empathy and Trust:

Effective feedback is rooted in empathy and trust. Creating a safe and supportive learning environment is essential for feedback to be received positively. Teachers should approach feedback with empathy, avoiding emotional reactions and prioritizing the emotional well-being of their students.

Integrating Feedback into Planning:

When planning lessons, educators should:

Set Clear Goals: Define learning objectives and success criteria to guide student progress.

Anticipate Misconceptions: Be prepared to address common misunderstandings and provide targeted support.

Establish Trust: Build a culture of trust and openness in the classroom to facilitate effective feedback exchanges.

Feedback Goes Both Ways:

Teachers should be open to receiving feedback from students. Seeking feedback encourages student engagement and provides valuable insights for improving teaching practices. Additionally, teachers can infer feedback by observing students’ understanding and addressing any gaps in comprehension proactively.

Conclusion:

Feedback is a cornerstone of effective mathematics education, fostering academic growth and cultivating a supportive learning environment. By prioritizing specificity, actionability, empathy, and trust, educators can create a feedback-rich classroom where every student has the opportunity to excel in mathematics.

Mathematics and engineering go hand in hand. Mathematics is an essential tool for engineers and plays a crucial role in helping students become better engineers. In this article, we will explore how math helps students become better engineers.

Understanding and Applying Principles:

Engineering is all about applying scientific principles to solve real-world problems. Mathematics is the language of science, and without it, engineers would not be able to understand the fundamental principles that govern the world around us. By studying math, students learn how to analyze and solve complex problems, which is a critical skill for any engineer. Moreover, math helps students understand the fundamental concepts of physics, which is essential to many engineering fields.

Analyzing and Solving Problems:

Engineers are problem solvers, and math is an essential tool for problem-solving. Math helps students develop critical thinking skills and teaches them how to analyze and solve problems systematically. Engineers use mathematical concepts to create models, analyze data, and make predictions. These models and predictions help engineers design and build products that meet specific needs and requirements. One standard approach to building your maths skills is by participating in Olympiads such as the International Maths Olympiad Challenge.

Design and Optimization:

Designing and optimizing systems is another essential part of engineering. Math plays a critical role in helping engineers design and optimize systems. Mathematical models help engineers simulate and optimize systems to ensure that they meet specific requirements. By understanding mathematical concepts like calculus, optimization, and linear algebra, students can learn how to design and optimize complex systems.

Communication:

Engineers must be able to communicate complex technical concepts to non-technical stakeholders. Math helps students develop this skill by teaching them how to use graphs, charts, and other visual aids to communicate complex data and concepts. By using math to present data and findings, engineers can help non-technical stakeholders understand the technical aspects of their work.

Mathematics is an essential tool for engineers. By studying math, students can develop critical thinking skills, learn how to solve complex problems, and design and optimize systems. Moreover, math helps students communicate complex technical concepts to non-technical stakeholders, an essential skill for any engineer. Therefore, it is important for engineering students to have a strong foundation in mathematics. By doing so, they can become better engineers and contribute to solving the world’s complex problems.

Mathematics is a significant aspect of developing technological advancements in children. Understanding the logic and concept of Math is important. And so is executing them in many useful areas. To participate and prepare for the International Maths Olympiads, it is essential to study mathematics comprehensively. Math preparation will help your child handle all academic career requirements.

The International Mathematical Challenge allows your child to upskill and understand the maths competition level that is taught in the classroom. For your child’s safe and robust future, as a parent, you must encourage them to participate in the International Maths Olympiad competition. Click here to register today.

Participating in international math Olympiads can benefit a child’s future. Some of the most important benefits of participating in math Olympiads include:

Improving Problem-Solving Skills: Math Olympiads involve solving complex and challenging math problems. This helps children develop critical thinking and problem-solving skills, which are important for success in many fields.

Enhancing Mathematical Knowledge: Participating in math Olympiads helps children learn new mathematical concepts and ideas and strengthens their existing knowledge.

Building Confidence: Solving challenging math problems can be difficult, but participating in math Olympiads helps children build confidence in their abilities to solve difficult problems.

Boosting Academic Performance: Participation in math Olympiads can improve academic performance in mathematics and other subjects.

Opportunities for Scholarships: High-performing students in math Olympiads may be eligible for scholarships and other academic opportunities.

Exposure to New Cultures: Math Olympiads are often international events, giving children the opportunity to meet and interact with students from different countries and cultures.

EndNote

Participating in math Olympiads can help children develop valuable skills and knowledge, build confidence, improve academic performance, and open up new opportunities for scholarships and international exposure.

Our laws of nature are written in the language of mathematics. But maths itself is only as dependable as the axioms it is built on, and we have to assume those axioms are true.

You might think that mathematics is the most trustworthy thing humans have ever come up with. It is the basis of scientific rigour and the bedrock of much of our other knowledge too. And you might be right. But be careful: maths isn’t all it seems. “The trustworthiness of mathematics is limited,” says Penelope Maddy, a philosopher of mathematics at the University of California, Irvine.

Maddy is no conspiracy theorist. All mathematicians know her statement to be true because their subject is built on “axioms” – and try as they might, they can never prove these axioms to be true.

An axiom is essentially an assumption based on observations of how things are. Scientists observe a phenomenon, formalise it and write down a law of nature. In a similar way, mathematicians use their observations to create an axiom. One example is the observation that there always seems to be a unique straight line that can be drawn between two points. Assume this to be universally true and you can build up the rules of Euclidean geometry. Another is that 1 + 2 is the same as 2 + 1, an assumption that allows us to do arithmetic. “The fact that maths is built on unprovable axioms is not that surprising,” says mathematician Vera Fischer at the University of Vienna in Austria.

These axioms might seem self-evident, but maths goes a lot further than arithmetic. Mathematicians aim to uncover things like the properties of numbers, the ways in which they are all related to one another and how they can be used to model the real world. These more complex tasks are still worked out through theorems and proofs built on axioms, but the relevant axioms might have to change. Lines between points have different properties on curved surfaces than flat ones, for example, which means the underlying axioms have to be different in different geometries. We always have to be careful that our axioms are reliable and reflect the world we are trying to model with our maths.

Set theory

The gold standard for mathematical reliability is set theory, which describes the properties of collections of things, including numbers themselves. Beginning in the early 1900s, mathematicians developed a set of underpinning axioms for set theory known as ZFC (for “Zermelo-Fraenkel”, from two of its initiators, Ernst Zermelo and Abraham Fraenkel, plus something called the “axiom of choice”).

ZFC is a powerful foundation. “If it could be guaranteed that ZFC is consistent, all uncertainty about mathematics could be dispelled,” says Maddy. But, brutally, that is impossible. “Alas, it soon became clear that the consistency of those axioms could be proved only by assuming even stronger axioms,” she says, “which obviously defeats the purpose.”

Maddy is untroubled by the limits: “Set theorists have been proving theorems from ZFC for 100 years with no hint of a contradiction.” It has been hugely productive, she says, allowing mathematicians to create no end of interesting results, and they have even been able to develop mathematically precise measures of just how much trust we can put in theories derived from ZFC.

In the end, then, mathematicians might be providing the bedrock on which much scientific knowledge is built, but they can’t offer cast-iron guarantees that it won’t ever shift or change. In general, they don’t worry about it: they shrug their shoulders and turn up to work like everybody else. “The aim of obtaining a perfect axiomatic system is exactly as feasible as the aim of obtaining a perfect understanding of our physical universe,” says Fischer.

At least mathematicians are fully aware of the futility of seeking perfection, thanks to the “incompleteness” theorems laid out by Kurt Gödel in the 1930s. These show that, in any domain of mathematics, a useful theory will generate statements about this domain that can’t be proved true or false. A limit to reliable knowledge is therefore inescapable. “This is a fact of life mathematicians have learned to live with,” says David Aspero at the University of East Anglia, UK.

All in all, maths is in pretty good shape despite this – and nobody is too bothered. “Go to any mathematics department and talk to anyone who’s not a logician, and they’ll say, ‘Oh, the axioms are just there’. That’s it. And that’s how it should be. It’s a very healthy approach,” says Fischer. In fact, the limits are in some ways what makes it fun, she says. “The possibility of development, of getting better, is exactly what makes mathematics an absolutely fascinating subject.”

HOW BIG IS INFINITY?

Infinity is infinitely big, right? Sadly, it isn’t that simple. We have long known that there are different sizes of infinity. In the 19th century, mathematician Georg Cantor showed that there are two types of infinity. The “natural numbers” (1, 2, 3 and so on forever) are a countable infinity. But between each natural number, there is a continuum of “real numbers” (such as 1.234567… with digits that go on forever). Real number infinities turn out not to be countable. And so, overall, Cantor concluded that there are two types of infinity, each of a different size.

In the everyday world, we never encounter anything infinite. We have to content ourselves with saying that the infinite “goes on forever” without truly grasping conceptually what that means. This matters, of course, because infinities crop up all the time in physics equations, most notably in those that describe the big bang and black holes. You might have expected mathematicians to have a better grasp of this concept, then – but it remains tricky.

This is especially true when you consider that Cantor suggested there might be another size of infinity nestled between the two he identified, an idea known as the continuum hypothesis. Traditionally, mathematicians thought that it would be impossible to decide whether this was true, but work on the foundations of mathematics has recently shown that there may be hope of finding out either way after all.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Michael Brooks*

Inspiring students to be exuberantly responsive is one of the most significant aspects of mathematics directions and a serious aspect of any curriculum. Successful teachers focus attentively on the less interested or weak students and the intelligent ones. Here are a few ways—based on intrinsic and extrinsic motivation—that can come into action to inspire primary and secondary school students in maths preparation.

Extrinsic and Intrinsic Motivation

Extrinsic motivation includes advantages that occur outside the student’s dominance. These may incorporate lucrative token rewards for top performance, escape “punishment” for accomplishing good, compliments for good work, and so on.

Although, many students show intrinsic motivation in their preference to understand a session or logic (task-related), to surpass others (ego-related), or to influence others. The ultimate aim gets to the barrier between intrinsic and extrinsic.

Strategies for Increasing Student Motivation in Math

Call attention to a gap in students’ skills: Disclosing to students a difference in their understanding abilities maximizes their desire to learn more. For example, you may present a few usual exercises or tasks that imply familiar circumstances, followed by exercises that include unfamiliar situations on the same maths topic. The more fiercely you find the gap in understanding, the more fruitful the motivation.

Display continuous achievement: Closely connected to the preceding technique is having students cherish a logical order of concepts. This varies from the earlier process in that it relies on students’ aspirations to increase, not complete, their knowledge skills. One instance of a sequential achievement method is how quadrilaterals differ from one to another from the point of view of
their properties.

Give a challenge: When students are challenged rationally, they respond with enthusiasm and attentiveness. Proper care must be taken in opting for the challenge for students like International Maths Olympiad Challenge offers maths test opportunities to students who want to prepare for the maths Olympiad from around the world. The maths challenge must lead into the curriculum and be within reach of the student’s abilities and grades.

Point out the usefulness of a topic: Introduce a practical implementation of genuine interest to the class at the start of a topic. For instance, in high school geometry, a student could be asked to find the diameter of a plate where all the relevant detail they have is a plate section smaller than a semicircle. The activity selected should be organized and easiest to motivate the students.

Use entertaining mathematics: Recreational motivation includes games, quizzes, contests, or puzzles. In addition to being chosen for their specific motivational advantage, these activities must be appropriate and uncomplicated. Effective implementation of this process will let students complete the recreation. Moreover, the fun and excitement that these recreational references create should be handled carefully.

Conclusion

Mathematics teachers must acknowledge the fundamental motives already exist in their learners or students who prepare hard to compete in International Maths Challenge. The teacher can then use these methods of motivation to increase engagement and improve the success rate of the teaching process. Utilizing student motivations and abilities can lead to the development of artificial mathematical problems and situations.

All kids are different and live with different skills and interests. Some kids are good at studies and some at sports, but no one can be good at everything. Many kids are good at mathematics, but many kids find maths a little confusing & challenging. There will be no other option for kids to skip this learning period; every kid has to learn all these subjects. Parents and teachers help their kids or students to learn these subjects with ease but there are a lot of ways by which students can easily enjoy these boring activities and enhance their learning skills.

Some of the ways to improve your child’s learning skills and abilities-

Visual Techniques

It’s a compelling technique to improve your kid’s learning skills. Generally, visual learners learn things by seeing what they are reading or writing. You should also provide your kid with all the tools and resources so they can learn hands-on. According to research, if kids have food like raisins or marshmallows on a daily basis, it can help them easily solve Maths Olympiad problems like addition or subtraction. This technique for addition or subtraction visually can upgrade your child’s understanding of maths skills and allow the child to become engaged in the process.

International Maths Olympiad Registration

Further, you can also register for the maths olympiad to enhance your child’s skills. These maths tests will help the child to build a positive perception regarding different subjects and enable them to think logically and achieve well in different phases of life.

Let them choose

One of the best ways for your kid to get engrossed in their studies is to let them choose their material and resources. They won’t even need to insist when they are already interested. It will be interesting for them, so they will pick up study material and read on their own. If you want your kid to solve IMO sample papers independently, you should first create interest. Allow them to pick books and find stories they can imagine.

Give them a reading book

All the kids need to know how to read, which is necessary for other learning activities. To improve a child’s performance, you should put a reading book in their room or motivate them to read books using the visualization technique. This will encourage them to read and solve IMO sample papers easily.

Create Environment

It’s essential to give them a clean and quiet environment to study so that they can give their complete focus without any distractions. Do they have proper space for books, computers, or laptops? Also, give them the required resources, like school supplies, folders, and International Maths Olympiad sample papers. So they don’t need to get up in the middle of their studies.

Allow them to ask for doubts

Your kid must feel free to ask you anything that they want. They should not hesitate to ask and provide them comfort so they can ask easily. Suppose they have any doubts in a lesson, you will be there and you should always be available for their help. This thing can also assist them to ask in their class without any hesitation.

Studying and preparing for the maths Olympiad will enhance students’ logical reasoning and thinking abilities and make them move toward strong career opportunities. If you are confused about participating in the International Maths Challenge, we are here to guide you at every step of your success. Click here to raise your query.

The International Math Challenge is administered across the world for students to acquire acknowledgment for their skills in mathematics. The exam is conducted at different grade levels and brings many possibilities for students to gain recognition, rewards, certificates, and even scholarships for further studies. One of the popular Maths challenges that nurture maths intellectuals is the International Math Olympiad. It is a big platform that concedes and rewards math masterminds worldwide. Candidates from more than a hundred countries join the Olympiad challenge every year.

Overview of Maths Olympiad

International Math Challenge is an ambitious exam that evaluates students for their mathematical talents and abilities. The main objective of this test is to inculcate a fierce mindset in students all over the world. Unlike school exams, Maths Olympiad tests are deliberated to unveil the real meaning of maths education. It offers a wider sight of math subjects and their empirical applications. Students who resolve problems intellectually using the acquired skills of math undoubtedly become problem-solvers.

Importance of Math Olympiad

Math Olympiad enhances the mathematical capability and competitive skills and knowledge of students. It allows them to find out their abilities and potential. Participating in such international competitive exams provides a strong fundamental for gaining an overall academic distinction. Students who participate in International Maths Olympiad acquire the confidence to answer difficult and complex questions. This gives them mastery over their competitors. Rewards and acknowledgment gained through the Maths Olympiad exam are highly beneficial in the academic portfolio and career planning of students.

Registration for Maths Olympiad

While many Maths Olympiad tests are held and administered through the school, some let children register individually. To get more information about the registration processes, students can visit our website.

Benefits of the International Maths Olympiad

Maths Olympiad is the type of platform that is excellent for enhancing the abilities and skills of your children. Students who join in Maths Olympiad exam have demonstrated increased marks in academics too. It is like an exam of a student’s mind of earlier learned concepts.

The International Maths Olympiad is an open manifesto for all students to examine their intellectual aptitude and talents. Preparing for the Maths Olympiad test qualifies students to inspect their math abilities against their fellows at school, national, and international standards. It allows students to know where they appear regarding their mathematical skills.

Finally 

Studying and preparing for the maths Olympiad will enhance the logical reasoning and thinking abilities of students and will make them move toward strong career opportunities. If you have any confusion in the process of participating in the International Maths Olympiad Challenge, we are here to guide you at every step of your success. Click here to raise your query.

The IMOC stands for International Mathematical Olympiad Challenge and is a well-renowned world championship mathematics competitive examination. It occurs every year, similar to another competitive exam. You can get ready for the International Maths Olympiad once you get familiar with the mathematical concepts and ideas, get into the mock tests, and try to give as many mock tests as you can.

Here are a few points that will help you prepare for the International Maths Olympiad:

Understand The Syllabus

While beginning to prepare for the International Maths Olympiad exam, it is necessary to introduce yourself to the syllabus. The syllabus for the exam is a bit different from your academic syllabus and you can find out all about it here.

Get The Expert Tutor

As your trainer will play a major part in your learning method, just be sure that you choose someone who is experienced and at par with your ease level. Generally, your school maths trainer can make your competition worthy. If you can’t find an experienced Maths Olympiad trainer near your location, look for the best online tutoring.

Learn Problem-Solving Skills

The IMC problem-solving approach is a one-stop solution for math competition practices and materials, thousands of students have already enrolled in the mission to crack the International Maths Olympiad. We have resources to learn how you can solve difficult types of math problems. Consult with our expert trainers and get a brief idea to use problem-solving skills in the examination.

Practice past papers

We do not wish to tutor your child; their teachers are doing a great job at it. We believe that students should be taught in only one way and not be confused with multiple styles of teaching. So while your child covers conceptual learning of math topics in school, we help you by providing exhaustive and fully solved Test Practice Papers (10 of them). These practice test papers are replicas of the Olympiad. Do not worry about the approach we have in our explanatory solutions. Our subject experts simply explain the basics using logical techniques which helps students to get well acquainted with the topics. Knowledge of these topics will eventually help students to ace their school curriculum as well.

Study Smart

Following your timetable, you also need to focus on sample papers and the previous year’s questions. Schedule mock tests that will let you track your progress report. Practice is the only key to success that will help in developing your skills. However, smart studying is just as essential as studying energetically. Find the sequence in the sample papers and utilize them to your greatest advantage.

Check Your Progress

Revision is an immensely significant part of preparing for the International Maths Olympiad. As you are learning, use note cards for writing down the major points. When you begin with revision, the note cards will let you remember the pointers that you have written down on the cards. The notes are an effective way of recalling what you have learned. Hence, if you are preparing for the International Mathematics Olympiad exam then you should always think that these revisions are the progress standard. If any such topics require you to check those pointers in the notes again and again, then go back to revise and focus on those questions a bit more.

Final Thoughts

The method of IMC preparation and taking part in our examination is a great learning experience apart from the result. This exam assists students to be skilled at school levels and provides them the opportunity to know the structure and timetable of international-level competitive exams. The IMO Challenge helps students throughout the world to determine their strengths and capabilities. 

Generally, the occurrence of students asking this question increases with growing age. Primary students know inside out that exams are very important. Brilliant middle school students consider a connection between their test results and semester mark sheets. Ultimately, upon graduation from secondary school, students have comprehended that the totality of their learning has less value than their results in the final exams.

Performance-Oriented Learning

Exam enthusiasm is an indication of performance-oriented learning, and it is intrinsic to our recent education management that needs standards-based reporting of student results. This focuses on performance apart from the method of learning and requests comparison of procurement amongst peers.

The focus for performance-aligned students is showing their capabilities. Fascinatingly, this leads to an affection of fixed mindset characteristics such as the ignorance of challenging tasks because of fear of failure and being intimidated by the success of other students.

Mastery-Oriented Learning

Mastery learning putting down a focus on students developing their competence. Goals are pliably positioned far away from reach, pushing regular growth. The phrase “how can this be even better?” changes the concept of “good enough”. Not to be bewildered with perfectionism, a mastery approach to learning encourages development mindset qualities such as determination, hard work, and facing challenges.

Most forms of mastery learning nowadays can be discovered in the work of Benjamin Bloom in the late 1960s. Bloom saw the important elements of one-to-one teaching that take to effective benefits over group-based classrooms and inspects conveyable instructional plans. Eventually, formative assessment was defined in the circumstances of teaching and learning as a major component for tracking student performance.

So where does mastery learning position in today’s classroom? The idea of formative assessment is frequent, as are posters and discussions encouraging a growth mindset. One significant missing element is making sure that students have a deep knowledge of concepts before moving to the next.

Shifting the Needle

With the growing possibilities offered by Edtech organizations, many are beginning to look to a tech-based solution like International Maths Olympiad Challenge to provide individualized learning possibilities and prepare for the maths Olympiad. The appropriate platform can offer personalized formative assessment and maths learning opportunities.

But we should take a careful viewpoint to utilize technology as a key solution. History shows us that implementing the principles of mastery learning in part restricts potential gains. Despite assessment plans, teachers will also have to promote a mastery-orientated learning approach in their classrooms meticulously. Some strategies are:

• Giving chances for student agency
• Encouraging learning from flaws
• Supporting individual growth with an effective response
• Overlooking comparing students and track performance

We think teaching students how to learn is far more necessary than teaching them what to learn.