ONLINE MATHEMATICS NOTES

Welcome!

Welcome to my online mathematics notes. I have designed this web site with you in mind. The intent of this site is to provide a complete set of free online notes.

I have tried to write the notes in such a way that they should be accessible to anyone wanting to learn the subject regardless of whether you are a learner or a teacher.

The field of mathematics studies a wide variety of topics besides just numbers. Mathematicians also study concepts like space, change and structure. Some even specialize in studying or finding patterns that can be used to formulate new theories.

You can see a complete listing of all available topics and able to read them for free. Examples in each topic are broken into steps to help you understand how and why mathematics works. Work the examples so that you understand the concepts and the methods presented. Ask yourself how new concepts relate to old ones. Make connections! As you practice the concepts presented on this web site, they will become part of your mathematical power.

I hope that this web site will help you make sense of the mathematics you learn. I want to enable you to tap into the power of mathematics.

All the topics available on this website are combined in the following common types of mathematics that exist:

Logic

Logic is a science that deals with the principles and criteria of validity of inference and demonstration: the science of the formal principles of reasoning. The study of logic originated in ancient Greece and has since been broken down into several types of fields, including syllogistic logic, computational logic and mathematical logic, among others. Some of the famous mathematicians who focused on studying logic during their careers include Aristotle, Avicenna and others.

Arithmetic

Arithmetic is a branch of mathematics that studies the numbers, especially the properties of operations between the numbers (addition, subtraction, multiplication and division). Arithmetic is a part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis.

Algebra

Algebra focuses on demonstrating the properties and relationships of abstract things in symbolic form. Graphing, absolute value equations and scientific notation are each an example of a topic in algebra.

Geometry

Geometry is the field of mathematics that deals with measurements. In geometry, students learn how to measure the surface area of an object and the volume of various objects. Geometry also deals with angles and the relationships between various points on a surface. Concepts from algebra are often used in solving geometrical problems.

Calculus

Integrals and derivatives are the fundamental objects of calculus. A definite integral is defined as a limit of Riemann sums. Differential calculus deals with studying the rate of change while integral calculus deals with the accumulation aspect of this mathematical field. In studying calculus, both geometry and algebra are used so it is important to have a full understanding of these two concepts before moving on to study this one.

Trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

Probability and Statistics

Probability and statistics are two separate fields of mathematics, but they are very closely related as studying statistics generally uses the idea of probability. But probability is not typically used in the study of statistics. Probability deals with the likelihood of something happening and this likelihood is often based on data found in certain statistics. The field of statistics focuses on separating and analyzing data to find trends and patters.

Important principles in teaching Mathematics

Principle 1: Let It Make Sense

Try alternating the instruction: teach how to solve a linear equation, and let the learner practice. Then explain why it works. As a teacher, don't totally leave a topic until the student both knows how and understands the why.

Principle 2: Remember the Goals

As teacher, you have to know your goals like

• enabling the learners to understand information around us,
• preparing learners for further studies in mathematics,
• letting learners see some beauty of mathematics and learn them to like it.

Principle 3: Know Tools

First of all teaher needs a chalkboard or paper to write on, instruments to be used like instruments of geometry and the book teacher is using. Then we have computer software, interactive activities, animated lessons and such. There are workbooks, fun books, work texts, books, and online tutorials.

Basic tools

• The board and/or paper to write on.
• The learners’ book and teacher’s guide

The extras

1. Computer and projector
2. Internet connection If computer lab is available at the school, teacher can show the learners how ICT is used in mathematics. For example
• Writing mathematical expression using Microsoft Office Word or other software tools like Math-Type,
• Sketching a function in Cartesian plane using Microsoft Office Excel,
• Determine the mean, standard deviation, variance,… of a set of data using Microsoft Office Excel formulas,
• Finding the limit and derivative of a function using MATLAB software…

Principle 4: Living and Loving Mathematics

As teacher, you have to

1. use math in daily life,
2. like mathematics,
3. love mathematics,
4. be happy to teach mathematics.

What can you do for slow learners?

Slow learners also want to learn mathematics, but lack of learning ability. Some techniques which can help slow learner are:

• More time to understand any problem or to find out the answer.
• Extra attention. With a small students group you can effectively respond each student.
• A fun environment for learners. Some mathematics games and activities can be used.
• Encourage learners to ask questions and let them feel free to ask for any help.
• Relating the new concepts with previous concepts. This will help them to catch the new concepts relatively fast.
• Explaining concepts using real life examples.
• Providing the opportunities to show them their work.
• Reviewing mathematics concepts time to time will allow them to master the math concepts.
• Rewarding them time to time this will help them to raise their confidence.

How do you get smarter in math?

As a learner, it is good to

2. make sure that you know what the words mean.
3. pay particular attention to learning the rules.
4. participate in class.
5. seek outside help.
7. attempt to solve all the problems that are given to you.
8. review your graded homework assignments when they are returned to you.

The many real world applications will let you see how you use mathematics in your daily life and give the foundation for the mathematics you will need in the future.

The applications you will find at the end of each topic will help you see why it is important to learn mathematics. The mathematics you learn here will prepare you for your future in our technological society. I wish you the best as you use this web site.

On Being a Learner

Those special teachers we know, with all the personal and professional qualities we admire, share another important feature that ensures their success: They possess very clear beliefs about learning. They have an understanding about how to beat customize content to fit the unique requirements of a situation and the capabilities of students. They are aware of the many obstacles to learning and know how to prevent potential problems before they occur. They know what learning is all about because they are committed, lifelong learners themselves.

On Being a Teacher

Who was the best teacher you ever had? Which mentor immediately stands out as the one who has been most influential and inspirational in your life? This could have been a teacher from Nursery School, or Primary School, or Secondary School, or High School or College. It could be a coach or a neighbor or a relative. Whoever it was, your teacher was someone who was an absolute master at helping you learn far more than you ever imagined possible.

On Struggling with the challenges of the Profession

Teaching, like any other profession, has its own unique set of challenges. Many of these challenges exist because teaching and learning are rooted in the human dimension. That means that we do not always act rationally, even when it might be in our best interests to do so. Likewise, schools are not entirely rational institutions; they are neither designed nor run with the efficiency and effectiveness that would be desired. In addition, there are many other challenges we face with a lack of resources, overcrowded classes, unmotivated students, uninvolved or over-involved parents, unsupportive colleague, insensitive administrators, and so on.

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