HOW TO STUDY COLLEGE

MATHEMATICSYour hack to mathematics

HOW IS COLLEGE MATHS IS DIFFERENT FROM HIGH SCHOOL MATHS ?

1. High school students don’t study maths theory( the major drawback),they just taught to get the problem done ,without even knowing how to tackle problem i.e. problem solving skills. But the college requires both.

2. High school students just learn a pattern ,may not be able to solve the surprise problems , but in college you are bombarded with the surprise problems daily so if you don’t learn how to approach problems you are not a college maths students.

NOTE :Maths=Mathematics

WHAT’S THE SOLUTION THEN ?DEFINITIONS

A definition in maths is a precise concept which describes some previously defined or undefined concepts as ‘number’ or ‘set’.

3 GOLDEN RULES TO DEFINITIONS

STEP 1:Make sure you understands what the definition says.

STEP 2:Determine the scope of the definition with examples.

STEP 3:Memorize the exact wording of the definition.

WHAT SHOULD YOU DO WITH A DEFINITIONS?

THEOREMS, PROPOSITIONS, LEMMAS, ANDCOROLLARIES

Definitions are useful but we need to relate them.

THEOREMS : Shows how do concepts solve problems.

PROPOSITIONS : Gives smaller results.

LEMMAS : Are technical results used in the proofs of theorems.

COROLLARIES : Are immediate consequences of theorems giving special cases.

STEP 1. Make sure you understand what the theorem says.

STEP 2. Determine how the theorem is used.

STEP 3. Memorize the statement of theorem.

FITTING THE SUBJECT TOGETHER.

STEP 1. Working backwards.

STEP 2. Making a definition-theorem outline.

HOW TO MAKE SENSE OF PROOF

STEP 1. Make sure you know what the theorem says.

STEP 2. Make a general outline of proof.

STEP 3. Fill in all the details.

DEVELOPING TECHNIQUES

STEP 1. Read through the theorems and examples.

STEP 2. Work enough problems to master the techniques.

STEP 3. Work a few problems in as many different ways as possible.

STEP 4. Make yourself a set of randomly chosen problems.

DON’T CRAM, LEARN HOW TO APPROACH PROBLEMS!

THANK YOU