 Mathematics
 96 (Registered)

13
Oct
$19.00
Applications and Interpretation: Course description
 Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures.
 This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a datarich world.
 It emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modeling. To give this understanding a firm base, this course also includes topics that are traditionally part of a preuniversity mathematics course such as calculus and statistics.
 The course makes extensive use of technology to allow students to explore and construct mathematical models.
 Applications and interpretation is a course aiming to address the needs of students who enjoy seeing mathematics used in realworld contexts and to solve realworld problems.
 Applications and interpretation at HL is a course aiming to address the needs of students with a strong mathematical background, who get pleasure and satisfaction when exploring challenging problems and who are comfortable to undertake this exploration using technology. The course gives great emphasis on modeling, statistics, and graph theory.
 Applications and interpretation at SL is a course aiming to address the needs of students who are weak in math and do not wish to undertake math after high school. The course gives a great emphasis on technology to solve practical problems.
The aims of all mathematics courses are to enable students to:
 develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power
 develop an understanding of the concepts, principles, and nature of mathematics
 communicate mathematics clearly, concisely and confidently in a variety of contexts
 develop logical and creative thinking, and patience and persistence in problemsolving to instill confidence in using mathematics
 employ and refine their powers of abstraction and generalization
 take action to apply and transfer skills to alternative situations, to other areas of knowledge and to future developments in their local and global communities
 appreciate how developments in technology and mathematics influence each other
 appreciate the moral, social and ethical questions arising from the work of mathematicians and the applications of mathematics
 appreciate the universality of mathematics and its multicultural, international and historical perspectives
 appreciate the contribution of mathematics to other disciplines and as a particular “area of knowledge” in the TOK course
 develop the ability to reflect critically upon their own work and the work of others
 independently and collaboratively extend their understanding of mathematics.
Course Content

Number and Algebra 0/15

Lecture1.1Scientific notation

Lecture1.2Arithmetic sequences and series

Lecture1.3Geometric sequences and series

Lecture1.4Financial applications

Lecture1.5Exponents and logarithms

Lecture1.6Approximation

Lecture1.7Amortization and annuity

Lecture1.8Equations and Systems

Lecture1.9Laws of logarithms

Lecture1.10Rational exponents

Lecture1.11Sum of infinite geometric sequences

Lecture1.12Complex numbers

Lecture1.13Modulus–argument (polar) form

Lecture1.14Matrices

Lecture1.15Eigenvalues and Eigenvectors


Functions 0/10

Lecture2.1Straight lines

Lecture2.2Concept of a Function

Lecture2.3The Graph of a functions

Lecture2.4Key features of graphs

Lecture2.5Modelling

Lecture2.6Modelling skills

Lecture2.7Composite functions and inverse functions

Lecture2.8Transformation of graphs

Lecture2.9Further modelling

Lecture2.10Scaling using logarithms and Linearizing data


Geometry and Trigonometry 0/15

Lecture3.1Threedimensional space

Lecture3.2Triangle trigonometry

Lecture3.3Applications of trigonometry

Lecture3.4The circle

Lecture3.5Perpendicular bisectors

Lecture3.6Voronoi diagrams

Lecture3.7Trigonometric ratios beyond acute angles

Lecture3.8Planar transformations

Lecture3.9Vectors

Lecture3.10Vector equation of a line

Lecture3.11Vector kinematics

Lecture3.12Products of vectors

Lecture3.13Introduction to graph theory

Lecture3.14Further matrices

Lecture3.15Graph algorithms


Probability and Statistics 0/19

Lecture4.1Collection of data and sampling

Lecture4.2Presentation of data

Lecture4.3Measures of central tendency and dispersion

Lecture4.4Linear correlation of bivariate data

Lecture4.5Probability and expected outcomes

Lecture4.6Probability calculations

Lecture4.7Discrete random variables

Lecture4.8The binomial distribution

Lecture4.9The normal distribution and curve

Lecture4.10Further linear regression

Lecture4.11Hypothesis testing

Lecture4.12Collecting and analyzing data

Lecture4.13Nonlinear regression

Lecture4.14Variance

Lecture4.15The central limit theorem

Lecture4.16Confidence intervals

Lecture4.17The Poisson distribution

Lecture4.18Population tests

Lecture4.19Markov chains


Calculus 0/18

Lecture5.1Introduction to differentiation

Lecture5.2Increasing and decreasing functions

Lecture5.3Derivatives of power functions

Lecture5.4Tangents and normals

Lecture5.5Introduction to integration

Lecture5.6Stationary points

Lecture5.7Optimisation

Lecture5.8Area of a region

Lecture5.9Further differentiation

Lecture5.10Further graph properties

Lecture5.11Further integration

Lecture5.12Area and volume

Lecture5.13Kinematics

Lecture5.14Differential equations

Lecture5.15Graphical approximations to differential equations

Lecture5.16Numerical solutions to differential equations

Lecture5.17Qualitative and analytical techniques for coupled systems

Lecture5.18Second order differential equations

Instructor
David is the professor of mathematics education at David School and a former Associate Professor of Physics at JNTU. He served as a teacher of mathematics and Physics in various international schools in Asia and Europe. His research focuses on social and cultural factors as well as educational policies and practices that facilitate mathematics engagement, learning, and performance, especially for underserved students. David School collaborates with teachers, schools, districts, and organizations to promote mathematics excellence and equity for young people.
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