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    *                Mathematical Science Advisor  
                                       *  Greater Memphis Metro Area - USA  *
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   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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                  Preparatory through Advanced University-Level Courses
                     Graduate School - Continuing Professional Education
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   *  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:  
   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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        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.   Degree Concentration:
           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.
           PREREQUISITES FOR: Physical science & scientific study programs;
           professional engineering fields, electronics-related fields;
           geosciences, biosciences & biomedical technology fields.

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