# How To Study Maths

Maths is considered to be one of the most scoring subjects. Some students love it, while there are many who hate to study this subject. It is important for students to have some proficiency in this subject as most courses include some level of mathematics and almost every profession uses it in some or the other way on a daily basis.

Many students find maths difficult as they don’t know the right way to study it to get good results. Maths is a subject which requires time and patience to master. There are several tips through which you can easily solve everyday math problems.

– Practice – Maths cannot be studied by just reading and listening. It is all about practice. The more you practice, the better it will be. There can be a number of ways of solving one math problem. Before taking any exam, it is important that you have solved a lot of problems beforehand. It is important to master one topic before moving on to the next topic.

– Learn the Basics – Never try to memorize the process of solving a problem. The most important thing to attain success in the long run is to focus on understanding the process and the logic behind it. Once you understand the basics of solving a problem, it will help you in understanding the approach of solving problems in the future. To be a master in this subject, it is important that you have a firm understanding of the key concepts, before moving on to solve more complex problems.

– Review your Mistakes – When you practice problems, it is important to go through the process one by one. If you make mistakes at any level, you should review them to understand where and how you went wrong. It is a great way to avoid same mistakes in future and polish your skills.

– Form a Study Group – You can form a study group with your friends to solve math problems together. When one person in the group has a problem, others can help him. Try to study in a distraction free environment as it is a subject which requires a lot of concentration.

– Create a Dictionary – Maths do involve a specific terminology. Create notes with all the concepts, terminology and definitions to consult them at any time.

You can also apply maths to solve real life problems to help change your perspective and think differently. You can easily learn maths by just taking one step at a time and practice regularly.

# Math Fun for Kids Gives Them a Head Start

Many parents give their children a head start in literacy by reading to them as toddlers, but mathematics is often reduced to just getting the children to count. Mathematics is far more than numbers and counting. Mathematical concepts can also be instilled in a pre-schooler and it doesn’t have to be boring; in fact it can be fun.

Here are three areas where parents and early education teachers can give young children a head start in mathematics:

Find math interactions in daily routines – Everyday activities can be chock-full of math. We use math all the time and don’t even know it or aren’t aware of it. We can help children develop simple math concepts by engaging them in activities that use math skills. This can be as simple as having your child find a matching pair of socks, shoes or even objects around the home. Maybe even have them help you sort out the laundry or organise silverware in a drawer. This will teach them sorting and comparing concepts.

Lunch or snack time can be a time of comparing who has the most crackers, carrot sticks, etc. Or juice in a glass can be observed as fractions, one-quarter full, one-half-full or three quarters-full. There are lots of things that we do mathematically and as you go through your daily routine, you will discover more and more things that you can bring to the attention of your child and engage the youngster which will develop their mathematical skills at an early age.

Playing with Math – Playtime affords plenty of opportunities for a child to engage and explore mathematical concepts. For example, shapes can be made with Play-Do, Popsicle sticks or other simple building materials. Story books or songs that include numbers are also excellent and fun ways to get a child to think mathematically. Songs such as Five Little Monkeys might be more educational than we think.

Math is more than Counting Numbers – Spatial reasoning and awareness are also valuable in mathematics. Although much of this is acquired as a child has the freedom to explore his surroundings, it can also be an object of childhood activities. Spatial awareness has to do with understanding objects as they relate to oneself in a given space.

When we discuss or give directives to children about an object’s location we are making them aware of objects in relationship to their space. For example, the ball is in the cupboard, the book is on the bookshelf, the toys are under the table are all examples of objects in location. Fun activities can include a game of hide-and-seek, the game Simon Says and other children’s games that include objects and movement in relationship to the child’s location.

These are only a few ideas of how you can give your child a head start in mathematics. As you look around, many other ideas, games and activities will come to your mind on how you can engage pre-schoolers so that their mathematical skills are developed. In the long-term, they will be better math students because math was taught to them in an enjoyable way.

# Pythogoreas Theorem and Trignometric Identities

Let ABC be a right angled triangle with angle ABC equal to 90 degrees. Let angle BCA be theta and it follows that angle BAC is equal to 90 – theta as the sum of the angles of a triangle is equal to 180 degrees.

Sin(theta) is defined as opposite side/hypotenuse and cos(theta) is defined as adjacent side/hypotenuse. Here the Adjacent side is BC, Opposite side is AB and the hypotenuse is AC.

Sin(Theta) = AB/AC; Cos(Theta) = BC/AC.. (1)

The pythogoreas theorem states that the square of the lengths of the opposite side and the adjacent side is equal to the square of the length of the hypotenuse.

So AB * AB + BC * BC = AC *AC – (2)

AB = AC * Sin(Theta) BC = AC * Cos(Theta)

So the RHS of the expression (2) can be rewritten as
AC * AC * Sin(Theta) * Sin(Theta) + AC * AC * Cos(Theta) * Cos(Theta). (3)

It follows from (2) and (3) that
(Sin(Theta) * Sin(Theta)) + (Cos(Theta) * Cos(Theta)) = 1.

This is the most fundamental identify in Trigonometry. All other identities follow from this.

Let us derive some more properties of trigonometric ratios.

Let us take angle BAC for consideration. Let us write down the expression for Sin(BAC) is equal to AB/AC =Cos(ABC). If Angle ABC = theta, then BAC = 90 – Theta. So Sin(90-theta) is equal to Cos(Theta) or in other words Sin(30) = Cos(60), Sin(60) is equal to Cos(30).

Let us now derive some more trigonometric identities such as Sin (A)/a, Sin (B)/b, Sin(C)/c etc.

Let Angle A be CAB, Angle B be ABC, Angle C be BCA
Sin (BCA) = AB/AC; Sin(CBA) = BC/AC.

Hence AB/Sin(BCA) = AC; BC/Sin(CBA) = AC;

So AB/Sin(BCA) = BC/Sin(CBA) implying that the ratio of Sin of an angle in a right angled triangle to the opposite side is equal. Now It has to be proved that this ratio also holds true for any other triangle, not only a right angled triangle. This can be done by drawing a perpendicular in case of non right triangles and deriving expressions for a/Sin(A), b/Sin(B) using two right triangles.

The values of trigonometric ratios such as sin, cos and tan for different values theta such as 30,45, 60 and 90 degrees Sin(30) can be found using the property of an isosceles /equilateral triangle.

An isosceles right triangle has two angles equal to 45 degree. If each side is equal to 1 the hypotenuse is equal to sqrt(2). So it follows that Sin(45) is equal to 1/sqrt(2).

The author is a dual master of science by research in Information Technology and Industrial Engineering. He has worked for many years in leading IT Services firms worldwide. He writes on academic theory, IT services, cricket and current affairs.