Prologue
Setting Hands-On Math Apart
Some Definitions from the Web
Science (from the
Latin scientia, meaning "knowledge") refers to any systematic knowledge
base or prescriptive practice that
is capable of resulting in a prediction or predictable type of outcome. In this
sense, science may refer to a highly skilled technique or practice.
Physics (Greek:physis
– φύσις meaning "nature") is a natural science it is the study of matter and its
motion through space-time
and all that derives from
these, such as energy and force.
More broadly, it is the general analysis of nature,
conducted in order to understand how the world and the
universe behave.
Mechanics (Greek
Μηχανική) is the branch of physics concerned with the behaviour of
physical bodies when subjected to forces or displacements, and the subsequent effect
of the bodies on their environment. The discipline has its roots in several ancient
civilizations. During the early modern period, scientists such as Galileo,
Kepler, and especially Newton, laid the foundation for what is now known as classical
mechanics.
Mathematics is
the science and study of quantity, structure, space, and change. Mathematicians
seek out patterns,
formulate new conjectures, and
establish truth by rigorous deduction from
appropriately chosen axioms and definitions.
Albert Einstein,
on the other hand, stated," as far as the laws of mathematics refer to reality,
they are not certain; and as far as they are certain, they do not refer to reality."
Applied Mathematics is
a branch of mathematics that concerns itself with the mathematical techniques
typically used in the application of mathematical knowledge to other domains.
Engineering
is the science, discipline,
art and profession of acquiring and applying technical, scientific and mathematical
knowledge to design and implement materials, structures, machines, devices, systems and processes
that safely realize a desired objective or inventions.
A Laboratory
(informally, lab) is a facility that provides controlled conditions in which
scientific research; experiments
and measurement may be performed.
A Common Teaching Method
Commonly, the topics and of mathematics, physics and engineering are taught separately.
Within a topic there will be history, concepts, logic-based derivations, examples worked
by the teacher and exercises to be worked by the student and graded by the teacher. Additionally, a topic may have an associated laboratory in which the students
are required to experiment, measure and report.
Setting HOM Apart
HOM is a scientific approach to conveying an understanding of physics
and mathematics
that employs "do it yourself" observations
on models that are based on the contributions to physics of such as Galileo,
Kepler, Newton and Lord Rayleigh, the contributions to applied mathematics by such
as Pythagoras and Gauss and the contributions of engineers such as Bush.
HOM's primary emphasis is on the use of applied mathematics in a computer-laboratory
environment to construct models of the physical relationships of force,
matter and motion in an atmosphere that provides both buoyancy and resistance to
motion. The use of a model atmosphere provides computer modeling that closely emulates
the physics of our real world. An even better model would include the effects
of Lift.
Deep understanding is acquired by constructing a model of a physical process,
by confirming that the model behaves in accord with its design objectives, by employing
the model to explore the laws and relationships that have been modeled and by using
the model to provide answers to new questions. Each of the foregoing factors,
constructing, confirming, exploring, and responses to "what if", makes a contribution
to a student's understanding of the behaviour of the world and universe in which
he lives.