For the full syllabus, see here.
These questions merely indicate the content of oral examinations. Exams are not limited to these questions. In general, and throughout the exams where appropriate, be prepared to speak about the relevance of the scientific material to philosophical, ethics, metaphysical, and theological questions (we call these “boundary issues”).
Examination of Biology Segments B1, B2, B3: Chemistry and Biochemsitry
What are fermions (leptons and quarks), bosons? What do they do, make, interact?
Explain why the periodic table arranged the way it is.
What is electron configuration for a given element? valence number? group? Calculate chemical formula for simple ionically bonded compounds based on valence numbers.
Describe the various types of chemical bonds and their relative strengths (ionic bonds, covalent bonds, hydrogen bonds, Van der Waal’s forces)
How does a chemical reaction work? What role does a catalyst play in a chemical reaction? What is a favorable reaction? How do you run reactions in unfavorable directions? Draw reaction energy diagrams.
Describe the four main macromolecules, their monomers, differences in their structure.
Describe the role of H+ bonding in macromolecular structure. Give two examples in:
Describe the cellular process of protein synthesis and where in the cell each step is occurring.
Examination of Biology Segments B4, B5: Cell Biology and Evolutionary Biology
Describe the types of cell. Describe the various parts of the cell (cell membrane, nucleus, mitochondrian, chloroplast, vesicular network, cytoskeleton) and give details about processes within each.
Distinguish between meiosis and mitosis. Outline the steps in each and the final outcome regarding the amount of cellular DNA present.
Describe cells in a functional context (either the immune system of the nervous system, depending on what was covered in class).
Summarize the work of Gregor Mendel. What two main principles of genetics were derived from his work (Independent Assortment and Segregation)? What is the molecular biological basis for these principles? What is an allele?
In mice there are two separate alleles for coat color and hair length. The dominant alleles are gray coat with short hair and the recessive alleles are tan coat with long hair. Work out a cross between a homozygous dominant mouse with a homozygous recessive mouse in the P generation and predict the allelic distribution in the F1 and F2 generations.
Summarize Darwin’s theory of natural selection. What evidence did Darwin adduce in support of it? What were its major flaws? What is the Modern Synthesis?
How does speciation occur? What are the factors relevant to population and evolutionary change?
Examination of Mathematics Segments M1: One-Dimensional Calculus
What is a function? Continuous function? Graph of a function? Tangent to a graph? Slope of a tangent?
How do the sine and cosine functions relate to the geometry of a circle? What are exponential and logarithmic functions and how do you calculate with them?
Define the derivative (from first principles). Describe the geometric meaning of a derivative and of the approximation method used to calculate it.
What are basic rules of differentiation? Basic derivatives? Differential equations?
Define the integral (from first principles). Describe the geometric meaning of an integral and of the approximation method used to calculate it. Distinguish definite from indefinite integrals. Explain area functions and their use in calculating definite integrals.
What are basic rules of integration? Basic integrals? Basic integration techniques?
What is an anti-derivative? State the fundamental theorem of calculus. Describe the relation between anti-derivatives and areas under curves.
Examination of Mathematics Segments M2, M3: Vector Calculus
What is a vector space? linear combination? linear dependence and independence? basis? dimension?
How do we define a metric on a vector space? Examples of metrics on R2, including graphs of length-1 vectors in Euclidean and Lorentzian metrics.
How do we use a metric to speak of length of vectors and angle between vectors? What is an orthonormal basis? coordinate system? How do we represent the same vectors in more than one coordinate system?
What is scalar (dot) product? vector (cross) product? linearity of an operation? test for orthogonality? right-hand rule? geometric and coordinate representation of dot product and cross product?
What are examples of functions with a variety of vector-space domains and ranges? vector fields and scalar fields? component scalar fields of a vector field?
What is directional derivative? partial derivative relative to a basis?
What is gradient? del? divergence? curl?
What is integral over a curve? a surface? a volume?
What is flux? circulation?
What is Gauss's theorem (divergence theorem)? Stokes’ Theorem?
Examination of Physics Segments P1: Electromagnetism
State Maxwell’s equations in differential and integral form. Show how to derive the integral from the differential form, and vice versa.
Explain the connection between Maxwell’s equations and the basic results of electrostatics. Derive Coulomb’s law from Maxwell I and Ampere’s Law from Maxwell II.
Write down the field equation for Electromagnetic radiation. (Bonus: derive it from Maxwell’s equations!) Explain the velocity of electromagnetic radiation from the field equation.
How do Maxwell’s equations establish the unification of light and electromagnetism? What is the significance of this result?
Examination of Physics Segments P2: Special Theory of Relativity
What is an inertial frame of reference? Principle of relativity? Galilean transformation?
State the postulates of STR. Describe the Lorentz transformation and its significance.
State the mechanical consequences of STR: relativity of simultaneity (via thought experiment), length contraction and time dilation (write up formulas), addition of velocities (write up formula).
State the dynamical consequences of STR: mass-energy equivalence (explain the energy triangle).
Describe experiments confirming STR.
What is a space-time diagram? Use one to explain the Lorentz Metric versus the Euclidean metric. Use one to explain the twin paradox.
What is the philosophical significance of STR for understanding space and time?
Examination of Physics Segments P3, P4: General Theory of Relativity and Cosmology
1. About tensors:
2. About the General Theory of Relativity:
3. Big-Bang Cosmology
4. Quantum Cosmologies
Examination of Physics Segments P5: Quantum Machanics
1. Early discoveries
1.1 Energy quantization of radiation
1.2 Interference effects of particles
1.3 Double-slit experiment (illustrates Heisenberg Uncertainty Principle)
1.4 Stern-Gerlach experiment (illustrates probabilities nature of measurement outcomes)
2.1 Mathematical interpretation of systems, states, observables, measurement
2.2 von Neumann's Hilbert Space approach
2.3 Born's Projection Postulate
2.4 Schrödinger's Equation
3.1 Einstein-Podolsky-Rosen thought experiment (1935): locality entails violation of uncertainty principle, which implies incompleteness of quantum mechanics
3.2 Bell's inequalities: locality entails that statistics from experiments on correlated particles pairs should conform to specific inequalities (but Aspect's experiments show they do not, thus demonstrating non-locality)
3.3 Non-locality and faster-than-light information transfer
4. Philosophical Interpretation
4.1 Three levels of interpretation
4.2 Major interpretations
4.3 Significance for theology (optional)
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