You are asking about millions of mathematical application in our life, like calculation of area, volume, velocity, acceleration ....etc.

Regards, Emad

I'm insterested in following application examples:

・Periodical cicadas

https://en.wikipedia.org/wiki/Periodical_cicadas

http://www.jstor.org/stable/2406568?seq=1#page_scan_tab_contents

・ Pattern of fish

https://en.wikipedia.org/wiki/Pattern_formation

Wonderful link about this interesting topic. Hope helps you.

http://www.educationworld.com/a_curr/mathchat/mathchat019.shtml

You are asking about millions of mathematical application in our life, like calculation of area, volume, velocity, acceleration ....etc.

Regards, Emad

Dear Ebadi,

Taking my case where I really need math for analysis and forecasting of my signals in order to perform "diagnostics and prognostics of rotating machine". Once, I was like some of your students wondering the usefulness of the math because I was "Solutions User" since I use only the available solutions to my problems but when you become "Solution Creator" then I needed badly many mathematical formula to analyse and model my problems and also in the way figuring out solutions.

Hope this will motivate your student ;)

You can study periodic traveling wave (PTW) which is found many natural phenomena. To study PTW, you can use some tools like auto-07p, matcont, FlexPDE, wavetrian1.2 etc. as bifurcation analysis.

You may visit the following link for more information.

https://en.wikipedia.org/wiki/Periodic_travelling_wave

Thanks.

Wonderful idea about this topic is "Fractal Geometry and Nature"  

What do you think then about autowave processes in media and objects of different nature?

https://en.wikipedia.org/wiki/Autowave

I've not caught any difference between autowaves and periodic travelling wave at first look. In any case they are of something very similar.

Mathematics in Biology, Mathematics in Physiology, Pattern formation (animal coat, Fruit skin), Mathematics in Computer Science , Mathematics in Business and economics could be good examples.

What about weather forecast...?

It also depends on your special mathematical topic.

Best Regards

Andreas

Yes the uinverse actually made of maths.

@ M.J.Ebadi

There are many examples . I give here two :

(1) When you go market to purchase few things

If you do not know addition , the shopkeeper will chit you.

(2) When you puchase a land you must know square feet area . Without math it is not possible .

(3) When you go to school , you must know

how to read time in your watch.

(4) How many finger's you have ?

There are many examples in day to day life

where you realise the importance of mathematics.

Lastly mathematics decorates physics .

B.Rath

There are many applications of pure mathematics in real life. Shapes of different particles are discuss through the concept of Group theory e.g the structure of benzyne are discuss through the symmetric groups more over the shape of triangle form dihedral group so we discuss all the possibilities of shape of triangle with prperties of group.

Необходимо обучить всех студентов теории голосования.

Обязателен курс лекций по теме "Как выигрывать выборы".

Эта тема должна стать не только инструментом в повседневной жизни , но и элементом культуры всего человечества. Все должны понимать, что выборы это не самый лучший метод поиска истины.

@M.J.Ebadi

One of the simple application of mathematics is to construct house of 1400 squareft in the area of 1600 sqft having three or four rooms.

Or construct a bridge with road having 45 ^° degree slope .

B.Rath

Дополнительное пояснение. Математический анализ демократии показывает, что она может быть так же смертельно опасна как игра в русскую рулетку. Для эффективности демократических процессов поиска истины необходимым условием является высокая культура и порядочность всех участников процесса.

For interesting math applications in real life, i suggest you to read this book

Applied Partial Differential Equations: A Visual Approach, Author: Peter A. Markowich

How about application of probability calculus? See how much you will have to pay before you win in lotto. Need more money? Then think about prediction of stock market using tools like genetic algorithms, neural networks, or - maybe - something even better.

Impedance matching for picking speakers appropriate to the radio/transmitter.

Fourier transforms to make streaming of music or video more efficient.

Launching and tracking of satellites.

The efficient design of cans and drinking bottles.

Trajectory profiles for realistic video games.

Determining a safe radius for roads and highways so that cars don't slide off the road by going around corners that are too sharp.

Basically, anything involving physics and chemistry is going to involve mathematics--which means everything.

You will find plenty of wonderful examples in this text: https://link.springer.com/book/10.1007/978-0-387-75340-9?no-access=true

Mathematical abstraction can even unravel the mysteries of nature. You can read this -

From n-qubit multi-particle quantum teleportation modelling to n-qudit contextuality based quantum teleportation and beyond.

Article From n-qubit multi-particle quantum teleportation modelling ...

@Sona Ahuja

Your suggested answer can hardly be visualised in day to day life . There are many people they do not use computer .

For example a farmer , who knows only addition, substraction . In which way your

answer will be helpful to understand the importance of mathematics . Hope you will realise it .

B.Rath

@M.J.Ebadi

Thank you . I feel your question related to common people's understanding in mathematics. Eventhough there are many applications of mathematics in our day to life , however realisation of its importance to ground level people is not an easy task . For example people in remote corners of world , who do not have any education but

do every thing in finger counting . They see the sun to realise time .etc

B.Rath

application of matrix in daily life in following link https://www.slideshare.net/moneebakhtar50/application-of-matrices-in-real-life

and some real life application are in following link

https://www.unbc.ca/math-statistics/real-life-applications-mathematics

There are alot of math applications, physics( dynamical systems, plasma, quatum), all engineering areas, .... see the applications of PDE.

Knowledge of the student community and culture Important

Maybe not too much numbers, equations, etc. but nevertheless mathematics: social networks.

@M.J.Ebadi

Recently while travelling from India to USA ; I notice math is very useful in knowing time in India when I am in USA.

B.Rath

There are alot of applications of math in real life. What's field do you carrying about?

Many mathematical applications to real life can be found in textbooks on physics: mechanics, molecular physics, optics, quantum and nuclear physics. What's field do you carrying about?

You can check this list: http://www.math.com.mx/aplicaciones_matematicas.html

For me it's applications can be somewhat hidden to 'many' people. U have to start from the background. When u start learning a, b, c or 1, 2, 3,... and try to see the reasons for introducing or creating them. What is the meaning of one 4th and why one 4th plus one 4th be equal an half? Why should we find the L.C.M or H.C.F? Why Calculus? Then u move further. U should be able to see reasons for introducing some topic. In computing I would say there are 3 maths, we have Calculus, probability and Linear Algebra. Another is set and the mathematical symbols...etc. When u know the rudiments u see truth and clarity and not probably "Magic" as some people think. U see the applications and to me when u discover these it can sound very very interesting and u appreciate the maths equations and models. The concept is the key. As a simple illustration, why introducing negative numbers? In real life it may mean negative number counts of things like number of things stolen in museums while positive number counts of things mean new things added to the museums. But the application of negative numbers is numerous, I think. Why introducing number lines? Why adding 2 axes usually called x and y axes? Why adding 3 axes? When could we have one or more axes? Do u know u can have 1 million axes? Why do we have negative numbers again on each axes? Sometimes Things becomes unclear if u can't answers 'why'. If u ask your self questions u can be forced to find the answer yourself, I guess. Then U might see the reality and applications. This is because all maths could have application to real life. I don't think I have been able to discover Maths that doesn't have application(s) to real life when ever I could answer my own "Whys". In Maths if u don't understand why some things (rudiments) are the way they are or used in a particular way, when u get to advanced level u might tends not to believe it since u don't see how the house is built from the beginning it becomes a problem to understand how the house is built or believe a theorem or the need for an equation. Which are of course, connected to applications of such things. So some of these things counts when looking for interesting applications. What is interesting to a researcher might not be interesting to you.