Mathematical Science Advisor
Greater Memphis Metro Area - USA
Site Hosted by :
M. A. Franklin, M.S, B.S.E.E.
Alumnus: Graduate School of Mathematics,
Georgia Institute of Technology, Atlanta, GA.
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Course Instruction - Mentoring - Program Advice
Preparatory through Advanced University-Level Courses
Graduate School - Continuing Professional Education
Independent Study Programs
To inquire about tutoring arrangements please see contact notes:
Session arrangements by Voice telephone contact (only).
Preparatory Level Courses and Related Topics
FOUNDATIONAL MATHEMATICS - PREPARATORY LEVEL:
(Foundational, Preparatory and introductory college levels)
SELECTED EXAMPLES OF TOPICS IN MATHEMATICS
Natural numbers & order. Primes & prime factors. Set operations. Venn diagrams.
Real number system: Properties & operations. Rational & irrational numbers.
Plane Geometry: Introductory Logic. Postulates & deductive process: Proofs.
Plane Geometry: Theorems. Congruence. Similarity. Symmetry. Angle measure.
Pre-Algebra to Algebra II. Equations: solutions. Functions & graphs. Trigonometry.
Simutaneous equations & applications: matrix operations: matrix algebra.
Pre-Calculus: Introductory Calculus: Limits, continuity, derivatives, integrals.
Exponential functions & natural logarithm. Definite integral: bounded areas.
Applications: Function graph analysis: maxima-minima, Infinite sequences & series.
Complex number system & complex plane: Operations: applications in algebra.
Physics applications: motion, velocity, acceleration. Vector & scalar quantities.
Finite Math: factorial notation: permutations, combingations: binomial coefficients.
Introductory Probability: computing probabilities. Distributions: normal curve.
Basic statistics: Sample spaces. Frequency charts; mean, standard deviation.
See additional topics under: "University Level Courses & Related Topics".
PHYSICS & CHEMISTRY: :
SELECTED EXAMPLES OF TOPICS IN PHYSICS
PHYSICS: Dimensional analysis: SI units. Scalar & vector quantities.
Physics: Coordinate reference frames: uniform motion; relative velocity.
Physics: Newton's Laws: Inertial Mass. Energy. Momentum. Conservation laws.
Physics: Static forces; torques; resolving components. Pressure: Gases; fluids.
Physics: Kinematic equations of motion. Constant acceleration; Circular motion.
Physics: Gravitational force & acceleration. Kinetic & potential energy; work.
Physics: Geometric Optics. Wave propagation: Sound. Properties of light.
Physics: Electric charge & current. Electric & magnetic forces. Electric circuits.
Physics: Relativity principles: Speed of light propagation: mass-energy relation.
Physics: Fundamental particles. Atomic nuclei. Radioactivity: half-life.
See additional topics under: "University Level Courses & Related Topics".
SELECTED EXAMPLES OF TOPICS IN CHEMISTRY
CHEMISTRY: (Stoichiometry. Atomic mass units; mole concept; molar mass.)
Chemistry: Periodic Chart: Elements & element group properties. Isotopes.
Chemistry: Electron configuration; orbitals & orbital quantum numbers.
Chemistry: Kelvin temperature scale, Ideal Gas Laws. Specific Heat. Enthalpy.
Chemistry: Covalent bonds. Ionic Bonds. Valence. Lewis dot structures.
Chemistry: Molecular bond types. Nomenclature of Covalent & Ionic compounds.
Chemistry: Valence bond theory. Electronegativity scale. Polar bonds.
Chemistry: VSEPR bond theory: Molecular structure. Molecular bond geometry.
Chemistry: Chemical reaction types & equations: balancing equtions.
Chemistry: Oxidation-Reduction. Oxidation states and oxidation numbers.
Chemistry: Acid-base chemistry: Brønsted-Lowry & Lewis theories.
Chemistry: Chemical thermodynamics: Entropy. Spontaneous reactions.
University Level Courses and Related Topics
MATHEMATICS COURSE AREAS: (SELECTED EXAMPLE TOPICS):
Introductory topics: Logic. Set Theory. Real & Complex number systems.
College Algebra: Coordinate Geometry. Functions. Relations. Trigonometry.
Introductory Calculus: Limits. Continuity. Derivatives. Integrals;
Exponential functions & logarithmic functions. Calculus applications.
Advanced Calculus: infinite sequences; infinite series: Taylor series.
Advanced Calculus: multi-variable & vector calculus; physics applications.
Advanced Calculus: Partial derivaties. Multi-dimensional integrals.
Probability Theory/-Applied Statistics. Finite Math. Linear programming.
Algebraic foundations: Theory of groups, rings, fields, vector spaces.
Linear algebra: matrix algebra: Linear transformations: Linear Operators.
Differential equations. Complex variables. Real & Complex Analysis.
Partial differential equations of mathematical physics.
PHYSICS COURSE AREAS: (SELECTED EXAMPLE TOPICS):
Math prerequisites: College Algebra & Trigonometry; Vector algebra.
Physics: Introductory topics: SI units of measure. Dimensional analysis.
Physics: Scalar & vector quantities. Concepts of mass, energy, forces:
Physics: Inertial Reference frames: Relative velocity, uniform motion.
Physics: Newton's Laws: Conservation Laws: Kinetic & potential energy.
Physics: Momentum. Total Energy & Work. Power. Conservative force fields.
Physics: States of matter: Kelvin Temperature. Density. Fluid pressure.
Physics: Gravitational force & Accelerated motion. Dynamic equations.
Physics: Wave properties: frequency, wavelength: Sound. Light. Optics.
Physics: Electromagnetic theory: Circuits. Electric & magnetic fields.
Related Mathematics: Multi-variable calculus; Vector algebra & vector calculus.
Related Mathematics: Differential equations & PDE's. Transformations.
Special Relativity: Space-time coordinates: Lorentz transform. Mass-energy.
Introductory Quantum Theory: Planck constant. Planck-Einstein relation.
Wave-particle duality: de Broglie wavelength. Uncertainty Principle.
Standard Model of particle physics; Fermion-Boson classification.
Nuclear transitions: Radioactive decay & element decay series: half-life.
Prerequisistes for scientific and technical fields: !B>
Prerequisites for sciences, technical & scientific programs:
Mathematics, physics & chemistry prerequisites for engineering,
geosciences, biosciences, electronics-related technical fields;
computer science: programming foundations; systems analysis.
Independent study programs: Continuing professional education.
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Contact Information & Email Contact Guidelines
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SITE SPONSOR: M. A. FRANKLIN -- ACADEMIC REFERENCES:
POST GRADUATE STUDIES IN MATHEMATICS:
Department of Mathematical Sciences, Florida Atlantic University.
M.S., APPLIED MATHEMATICS,
Graduate School of Mathematics,
Georgia Institute of Technology. Degree Concentration:
Applied Mathematics: Mathematical Physics. Real/-Complex Analysis:
Functional Analysis. Topology. Lebesgue Measure Theory.
Thesis research field: Operator Theory: Hilbert Space theory:
Spectral representation of operators; Operator-valued integrals:
Gelfand Theory of Banach Algebras: Generalized analytic functions.
B.S., ELECTRICAL ENGINEERING.
Physics. Mathematics. Advanced Engineering Mathematics.
General & Analytical Chemistry. Engineering Thermodynamics.
Electromagnetic field theory. Electronic Circuit theory. Control Systems:
Frequency domain analysis. Computer science: Scientific programming.
RELATED SCIENTIFIC INTERESTS:
History of Theoretical Physics.
Physical Chemistry. Organic Chemistry. Biochemistry.
Computer science: Systems Analysis. Scientific applications.
INSTRUCTOR: PREPARATORY LEVEL - ADVANCED UNIVERSITY LEVEL:
STANDARD PROGRAM COURSES & FOUNDATIONAL COURSES:
MATHEMATICS & SCIENCES: standard preparatory & college curriculum.
Mathematics foundations: Logic. Set theory. Axiom systems.
Geometry (Euclidean Geometry): Multi-dimensional geometry.
Algebra: College Algebra: Coordinate Geometry. Trigonometry.
Pre-Calculus foundational topics. Introductory Calculus.
Advanced Calculus. Finite Math: Combinatorics-Graph Theory.
Probability theory. Real & complex analysis: Linear algebra.
Differential Equations, PDE Applications in physics.
PHYSICS. CHEMISTRY & PHYSICAL CHEMISTRY.
Mathematics for Physics, Chemistry & Engineering.
Physical science & scientific study programs;
professional engineering fields, electronics-related fields;
geosciences, biosciences & biomedical technology fields.
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