Mathematics Department

Mathematics is taught at St. Anselm's in the traditional way, building strong foundations in Algebra, Geometry, and Calculus which give our students the tools needed to make predictive analyses of their world.

Department Overview

Every student has math class every day, and all students take an Advanced Placement Mathematics course their senior year with ninety-five percent taking AP Calculus. Technology is implemented to augment, but not replace, the classical formalism of Mathematics.


Curriculum Sequence

Form A Fundamentals of Math
Form I
Pre-Algebra
Form II
Algebra
Form III
Algebra II & Trigonometry
Form IV
Geometry
 Form V  AB Pre-Calculus or BC Pre-Calculus and AP Calculus I BC
 Form VI
AB Pre-Calculus students: AP AB Calculus or AP Statistics
BC Pre-Calculus students: AP BC Calculus II; Calculus III (Multivariable)*
*Instructor permission needed

Course Descriptions

Fundamentals of Math

The introductory course in the St. Anselm's mathematics sequence. Over the year, students will build confidence in understanding and applying the fundamentals of advanced arithmetic and basic geometry. Topics to be studied include: Fractions, decimals, rational and irrational numbers, probability, combinations and permutations, areas, and volumes. 

Course Length: All Year

Registration Policy: Required for Form A



 

Pre-Algebra

This course finalizes students’ foundation in arithmetic and provides an introduction to Algebra. Topics covered include: introduction to signed numbers, arithmetic operations, introduction to variables, simple one-variable equations, simple geometric figures and their measurements, ratio, percent and probability.

Course Length: All Year
Registration Policy: Required for Form I



Algebra I

This course, which covers the full Algebra I textbook, will help students to become comfortable with symbol manipulation and the idea of a quantity without a fixed value. Topics covered over the year include: variables, fundamental and distributive properties, exponents, adding, subtracting, multiplying and dividing polynomials, factoring, linear and quadratic equations, word problems, inequalities, and systems.

Course Length: All Year

Registration Policy: Required for Form II




Algebra II & Trigonometry

A continuation of the students' study of algebra which begins to explore higher-order equations and the concept of complex numbers. Topics covered over the year include: division of polynomials, factoring to solve third-degree and higher polynomials, irrational and complex numbers, algebraic fractions, trigonometric functions, exponential and logarithmic functions, sequences and series, statistics and probability. 

Course Length: All Year

Registration Policy: Required for Form III




Geometry

This course exposes students to the principles and applications of common geometric operations in two and three dimensions. Students embrace an intuitive and axiomatic approach to the material, studying truth tables and symbolic and syllogistic arguments. The focus of the course will be on traditional Euclidean geometry, including theorems on lines and planes, angles, constructions, areas and volumes, coordinate geometry and trigonometry. The course concludes with a section in preparation for pre-calculus, including sequences and series, matrix algebra, probability theory, and analytic geometry.

Course Length: All Year
Registration Policy: Required for Form IV

Pre-Calculus (AB)

This is a course in algebra designed to introduce and develop those topics that are used in higher math and includes limits, the analysis of rational and polynomial functions, transcendental functions including the exponential, logarithmic, trigonometric and complex. Considerable attention will be placed on the trigonometric functions including the derivation of the laws of sines and cosines and an introduction to vectors. Systems of equations will be studied including both equalities and inequalities. Matrix methods will be developed for the solution of the systems. Finally, there will be an in-depth study building on previous study of sequences, series, probability and analytic geometry.

Course Length: All Year
Registration Policy: Mathematics option for Form V

 

Pre-Calculus (BC)

This course is identical to the (AB) course except that it will be taught in one semester. In the second semester students will take the first year college course in differential calculus.

Course Length: Fall Semester
Registration Policy: Mathematics option for Form V

 

AP Calculus (AB)

This course covers the material found in the first year of basic college calculus. It includes the theory of the derivative and its uses in finding the maximum and minimum of functions, the tangents to curves, how the change of one function is related to the change in another function and includes application to the sciences. In the second semester the integral is developed and is applied to the problems of finding areas, length of curves, volumes and surface areas. Other topics include: Limits, continuity, derivatives, mean value theorem, related rates, min-max, inflection points, derivative tests, applications to geometric systems, optimizing, graphing, integrals, areas, volumes, techniques of integration, separable differential equations, improper integrals.

Course Length: All Year
Registration Policy: Mathematics option for Form VI

AP Calculus (BC) I

A second-semester follow-up to the students' course in Pre-Calculus (BC). In this fast-paced course, students will become fluent in the vocabulary, principles, and procedures of introductory calculus. Topics to be covered include: Limits, continuity, derivatives, mean value theorem, related rates, min-max, inflection points, derivative tests, introduction of the integral.

Course Length: Spring Semester
Registration Policy: Prerequisite: Pre-calculus (BC); Mathematics option for Form V

AP Calculus (BC) II

This is a continuation of the Calculus (BC) I which was begun in the second semester of Form V. The theory of the integral and its use to calculate averages of continuous functions, areas, length of curves, volumes, and surface areas are discussed. Other topics include theory of integration, methods of integration in Cartesian and polar coordinates, geometric and scientific applications of integrals, parametric equations, improper integrals, differential equations, numerical methods, infinite series, Taylor’s theorem, harmonic, geometric, alternating, power, and convergence in integrals.

Course Length: All Year
Registration Policy: Prerequisite: AP Calculus I (BC); Mathematics option for Form VI

 

AP Statistics

This is an introduction to Statistics and is equivalent to the first year college course, although it is more conceptual in nature and less focused on software and formulas than many introductory courses. The basic techniques of hypothesis testing are covered and the conceptual framework is built slowly and emphasized. Other topics include Treatment of data, graphical display, standard deviation, correlation, regression, experimental design, survey sampling, normal and binomial probability models, simulation, and confidence intervals. The course is not as mathematically rigorous as the calculus; it places greater demands on communication skills so that the students can explain the concept of data analysis, form conclusions, support these conclusions with statistical facts and explain what these conclusions mean to others to make them better consumers of statistical information.

 

Course Length: All Year
Registration Policy:  Mathematics option for Form VI

 

Multi-Variable Calculus

This advanced course, which requires departmental permission, covers the material of a third semester college calculus class. The emphasis is on the vector approach to three dimensional systems and the calculus that applies to them. Topics include: Differentiation of scalar functions of two and three variables, min-max theory in 3-space, integration in 3-space using orthogonal coordinate systems (Cartesian, cylindrical, and spherical), vector products (dot, cross, and combinations), development of the vector derivative, gradient, divergence, curl, vector integrals, Green’s/Stokes' theorem, use of these techniques in the analysis of the solutions of the wave equation in classical and quantum mechanics, introduction to curvilinear coordinates and tensor calculus.

Course Length: All Year
Registration Policy: Prerequisite: AP Calculus II (BC) with Departmental Permission; Mathematics option for Form VI


Mathematics Faculty
Mr. John Corrigan, '83, Department Chair
Algebra I; Pre-Calculus (BC); AP Calculus (BC) I & II
B.S., Physics, University of Maryland
jcorrigan@saintanselms.org
Mr. Chris Battle
Mathematics

B.A., Biology, Johns Hopkins University
cbattle@saintanselms.org

Mr. Paul Commins
Algebra II/Trigonometry; AP Statistics
M.S., Statistics, University of Minnesota
B.A., Mathematics, Grinnell College 
pcommins@saintanselms.org
Mr. Bill Crittenberger
Pre-Calculus AB, AP Calculus (AB) 
M.S., Education, Johns Hopkins University
M.A., History, Yale University
B.A,, Journalism, George Washington University
bcrittenberger@saintanselms.org

Mr. Michael Manglitz, '00
Pre-Algebra
M.Ed. Reading Instruction, Goucher College M.A.
English Literature, The Catholic University of America B.A.
English Literature & Secondary Education, Goucher College
mmanglitz@saintanselms.org

Mr. John Montroll 
Geometry, AP Calculus (AB)
M.A., Applied Mathematics, University of Maryland
M.A., Electrical Engineering, University of Michigan
B.A., Mathematics, University of Rochester 
jmontroll@saintanselms.org
Dr. Herbert T. Wood
Multi-Variable Calculus
Ph.D., Physical Chemistry, University of Wisconsin, Madison
B.Ch.E., Chemical Engineering, Catholic University of America
hwood@saintanselms.org