This guidance is specially intended for students following courses related to advanced mathematics but it may also be helpful for a person at any level to update knowledge of the subject. This is not a textbook, this is a collection of articles (120 pages covering 58 topics) which is prepared to give unique experience which cannot be gained by traditional tutorials, notes, past papers, and model papers.

More challenging questions are incorporated as examples to illustrate how unconventional methods and nontraditional methods can be applied to find answers giving much freedom for your brain to get it programmed because brain researchers have recovered that even structural changes of the brain can be caused by giving proper exercises to it.

Each article in this series encourages thorough study and a full understanding of the concepts involved, and is designed as a study aid empowering you not only throughout your advanced level studies but also in university level. A variety of questions and alternative methods of proofs give this series a flexibility which you can use according to your knowledge and requirements. Practical applications are included to enhance mathematical skills and to develop interest in the subject. The context of this series may be helpful to get knowledge of how the principles and concepts were developed in mathematics over the generations and thereby to gain a vision in studying advanced mathematics.

To get the full use of this series you are strictly advised not to refer given answers without genuinely trying by yourself. Since this series is prepared to be given to students in section wise and not as a single document, pages are numbered separately in each article. (Can be given to students as extra activity when the subject teacher is absent or displayed in a notice board specially for advanced level maths classes)

Even after the most careful checking it is quite possible that some errors have been overlooked, and I shall be greatly indebted to anyone submitting suggestions to my mail address, janakarodrigo123@gmail.com.

My grateful thanks are due to the Rev.Bro.Dr.Pubudu Rajapaksha the Director of St. Benedict’s college, Rev.Bro. Henry Dissanayake a former Director of the college, Sectional Supervisor Mr. Tyrone Perera and Director of Mathematics ~ Zonal Education office (Colombo) Mr. Pushpakumara for the encouragement received. It would be a great mistake if I not mentioned Mr.H. Aberathne without his assistance definitely it would have been impossible for me to come out from the conventional frame and look into different types of challenging questions which I wanted to answer in my advanced levels.

I was really fortunate to receive the greatest assistance ever in my teaching career over three decades thanks to the Head/ Senior lecturer Dr.(Mrs.) Kissani Perera. Without having any knowledge about me she realized the importance of the document and decided to give her precious time to review it. I am also grateful to Lecturer Kapila Silva for the generous assistance in reviewing and professor Chula Jayawardene for the most encouraging thoughts.

Reviewing advanced mathematics document is a real challenge. If you take negatively it can be a risk but if you take positively I would say it is a great commitment to the subject Mathematics.

JANAKA RODRIGO
St. Benedict’s College
Colombo – 13
First print – 2021