Mathematics Mastery

Numbers = Number theory Formulas and related structures = Algebra Shapes and spaces = Geometry Quantities and their changes = Analysis

Axioms = Entities that are stipulated to have certain properties Proof = A succession of applications of deductive rules to already established results Theorems = Results that have been previously proved Abstraction from nature = Some basic properties that are considered true starting points of the theory

Involves the discovery of properties of abstract objects = Most mathematical activity Involves the use of pure reason to prove properties = Most mathematical activity Consists of a succession of applications of deductive rules to already established results = Proof Results include previously proved theorems, axioms, and basic properties = Proof

<p>Number theory = Subdiscipline of mathematics that deals with numbers Algebra = Subdiscipline of mathematics that deals with formulas and related structures Geometry = Subdiscipline of mathematics that deals with shapes and the spaces in which they are contained Analysis = Subdiscipline of mathematics that deals with quantities and their changes</p> Signup and view all the answers

<p>Most mathematical activity = Involves the discovery of properties of abstract objects and the use of pure reason to prove them Proof = Consists of a succession of applications of deductive rules to already established results Number theory = Deals with numbers Geometry = Deals with shapes and the spaces in which they are contained</p> Signup and view all the answers

<p>Probability of an event = A number between 0 and 1 that indicates how likely an event is to occur 0 = Indicates the impossibility of an event 1 = Indicates the certainty of an event Fair coin toss = An example where the probability of 'heads' equals the probability of 'tails', which is 1/2</p> Signup and view all the answers

<p>Event = Something that happens or is regarded as happening Axiomatic mathematical formalization = A systematic method of describing a concept or theory, using a set of axioms or rules Probability theory = The branch of mathematics that studies the likelihood of events Outcome = The result of a single trial of an experiment or study</p> Signup and view all the answers

<p>The higher the probability, the more likely the event will occur = Probability of an event Number between 0 and 1 = Probability Systematic method of describing a concept or theory = Axiomatic mathematical formalization Study of the likelihood of events = Probability theory</p> Signup and view all the answers

<p>The probability of an event is 0.5 = The event is equally likely to occur or not occur The probability of an event is 0.1 = The event is unlikely to occur The probability of an event is 0.9 = The event is highly likely to occur The probability of an event is 0 = The event is impossible to occur</p> Signup and view all the answers

<p>Tossing a fair coin = 0.5 Rolling a six-sided die and getting a 7 = 0 Getting a 3 when rolling a fair six-sided die = 1/6 Picking a card from a standard deck and getting a heart = 1/4</p> Signup and view all the answers