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History, theory, and practice of human and machine translation.

493. Readings in Linguistics. (l-3:0:Arr.) Blair

525. Descriptive Phonology. (3:3:0) Lytle

The structural description of the sound systems of language.

527. Descriptive Morphology. (3:3:0) Blair

The structural description of linguistic forms.

528. Syntax. (3:3:0) Prerequisite: Ling. 527. Lytle

Fundamental approach to generative grammar. Techniques of analysis
of linguistic data and preparation of grammatical statements through
ordered rules.

529R. Linguistic Structures. (3:3:1 ea.) Blair, Lytle

A consideration and comparison of the phonological and morphological
structures of several non-Indo-European languages. Students work with
native informants.

623. Problems in Contrastive Linguistics. (3:3:0) Bleiir

Contrast of structures in English and selected languages and the develop-
ment of grammatical description from these contrasts. Offered 1973 and
alternate years.

626. Problems in Historical Linguistics. (3:3:0) Lytle

Offered 1972 and alternate years.

693. Seminar in Linguistics. (2:2:0) Blair

Discussion of selected topics in linguistics.

699. Thesis for Master's Degree. (l-6:Arr.:0)



MATHEMATICS 387



Mathematics



Professors: Burton, Feamley, Fletcher, Hillam (Chairman, 290 MSCB), Jamison,
Moore, Robinson, Yearout.

Associate Professors: Gee, Gill, Hansen, Higgins, Larsen, Olpin, Peterson, Skarda,
Snow, Wickes.

Assistant Professors: Armstrong, Campbell, Chatterley, Ferguson, Garner, Ham-
ilton, Haupt, Lamoreaux, Tolman, Walker, Walter, Wight, Wynn.

Instructor: Mouritsen.

The Mathematics Department offers courses leading toward the Bachelor of
Science and Master of Science degrees in mathematics and the Bachelor of Arts
and Master of Arts degrees in mathematics education.

Requirements for the Bachelor of Science Degree in Mathematics

An undergraduate student majoring in mathematics must present a program
prepared in consultation with an adviser appointed by the department. He must
complete his program with a grade average of C or better. The following are
required:

1. Math. 141, 142, 243. 244, 332, 371, 541, and either 372 or 542.

2. A minimum of 15 additional hours selected with prior approval of the de-
partment from Math. 372, 387, 411, 412, 434, 436, 451, 452, 501, 502, 508,
542. 551, 552.

In addition to the courses listed above, each departmental major is required
to pass a written comprehensive examination during the first semester of his
senior year.

Suggested Program: The following program is given as a guide in planning for
those who wish to major in mathematics:

Freshman Year F W P.E i i

Math. 141, 142 4 4 Dev. Assy I i

English 3 3 Electives 6 5

Relig. 121. 122 2 2

Health 130 2 Total hours 18 18

Hist. 170 3

If a student has not had adequate preparation in mathematics to permit
him to begin his college work at the level of analytic geometry and calculus, he
should substitute the necessary prerequisite courses for Math. 141 in the above
program. However, he should realize that as a consequence, additional time
will probably be required to complete all the requirements for graduation.

Majors in mathematics are encouraged to take advantage of the four hours
of religion credit that may be earned by attending the devotional assemblies
during each of the four years of the undergraduate program.



388 MATHEMATICS



In selecting courses to meet the physical science group requirement, a mathe-
matics major should consider only the following: Chem. 105, 106, or 111, 112;
Physics 121, 122, 221, 222, or 211, 213, 214.

All students who contemplate pursuing graduate work in mathematics are
urged to complete both Math. 372 and 542 and to gain competence in French,
German, or Russian while an undergraduate.

Requirements for the Bachelor of Arts Degree in Mathematics Education

An undergraduate major who wishes to teach mathematics in secondary schools
must present a program prepared in consultation with an adviser appointed
by the Mathematics Department. He must complete his program with a grade
average of C- or better. The following are required:

1. Math. 112, 113, and 214; or 141, 142, 243, and 244 or the equivalent.

2. Math. 301, 302, 371, and 451.

3. A minimum of nine semester hours selected from the following: Math. 210,
300, 332, 372, 385, 387, 411, 434, 452, 501, 502, 412, 541, 542, 551, 552.

4. A teaching minor as described in the Education section of this catalog.

In order to obtain the Bachelor of Arts degree in mathematics education, a
student must complete the teacher certification requirements outlined by the
Education Department.

Suggested Program: The following program is given as a guide in planning
for those who wish to major in mathematics education:

Freshman Year F W Hist. 170 3

Math. 112, 113 P.E i i

(or 141, 142) 4 4 Dev. Assy I i

English 3 3 Electives 6 5

Relig. 121, 122 2 2

Health 130 2 Total hours 18 18

If a student has not had adequate preparation in mathematics to permit him
to begin his college work at the level of analytic geometry and calculus, he
should substitute the necessary prerequisite courses for Math. 112 in the above
program. However, he should realize that as a consequence, additional time
will probably be required to complete all the requirements for graduation.

Undergraduate Minors

A student who majors in mathematics is not normally required to have a minor
but should work closely with an adviser to plan a program of elective courses
that meets his own educational objectives. A student who majors in mathe-
matics education, however, is required to have a teaching minor and should
consult the Education section of this catalog.

A student who wishes to minor in mathematics must complete with a grade
average of C- or better —

1. either of the sequences Math. 141, 142, 243; or Math. 112, 113, 214; and

2. a minimum of 9 additional credit hours in courses selected from the following:
Math. 244, 300, 332, 371, 372, 387, 411, 412, 434, 436, 451, 452, 501, 502,
508, 541, 542, 551. 552.

Graduate Degrees

The Department of Mathematics offers courses leading to the degrees of Master
of Science in mathematics and Master of Arts in mathematics education. Com-
plete details are available in the Graduate School Catalog.

Courses

90. Algebra. (0:3:0)

Equivalent to first year high school algebra.



MATHEMATICS 389



91. Plane Geometry, (0:3:0)

Equivalent to high school plane geometry.

97. Mathematical Review. (0:3:0) Prerequisite: Math. 111.

Review of mathematics through calculus. Primarily for returning
missionaries and others. Offered on the block plan.

101. Intermediate Algebra. (3:5:0) Home Study also. Prerequisites: Math.
90 and 91 or equivalent.

Equivalent to second year high school algebra.

105. College Algebra. (3:4:0) Home Study also. Prerequisite: Math. 101
or two years of high school algebra and one year of plane geometry.

Parallels part of Math. Ill at slower pace.

106. Trigonometry. (3:3:0) Home Study also. Prerequisite: Math. 105.

Parallels part of Math. Ill at slower pace.

108. Basic Analysis. (4:4:1) Prerequisite: Math. 101 or two years of high school
algebra.

Introduction to logic, matrix algebra, linear programming, and ele-
mentary functions. For students of business or social science.

109. Introduction to Calculus. (4:4:1) Prerequisite: Math. 108 or 111.

Introduction to plane analytic geometry and one-dimensional calculus.
Primarily for students in the colleges of Biological and Agricultural Sci-
ences and Business.

111. College Algebra and Trigonometry. (5:4:2) Home Study also. Prerequi-
sites: Math. 101 or two years of high school algebra and one year of plane
geometry.

112, 113. Analytic Geometry and Calculus I, 11. (4:4:0 ea.) Prerequisite: Math.
Ill or equivalent.

Plane analytic geometry; one-dimensional differential and integral calcu-
lus, with applications.

121, 122. Technical Mathematics. (3:2:3 ea.) Prerequisite: Math. 101.

College algebra, trigonometry, analytic geometry, and an introduction
to calculus. Problems and applications. Primarily for students in industrial
and technical education.

141, 142. Introduction to Calculus and Analysis. (4:4:0 ea.) Prerequisite: Math.
Ill or equivalent.

Plane analytic geometry and one-dimensional calculus, with applications.
Primarily for mathematics majors.

205H. Structure of Mathematics. (3:3:0)

Consideration of the structure and meaning of mathematics. For Honors
students who are taking no other mathematics courses.

210. Introduction to Mathematical Logic. (3:3:0) Prerequisite: Math. 105 or
111.

Traditional logic. Boolean algebra, algorithms, Turing machines.

214. Analytic Geometry and Calculus III. (3:3:0) Home Study also. Prerequi-
site: Math. 113.

Multidimensional calculus, infinite series.

223. Technical Mathematics. (3:3:0) Prerequisite: Math. 122.

Analytic geometry and calculus. Primarily for Technical Institute stu-
dents.

224. Numerical Methods in Technology. (3:3:0) Prerequisites: Math. 223 and
Comput. Sci. 231.

Interpolation, approximation, numerical differentiation and integration,
linear programming, solutions of equations. Primarily for students in in-
dustrial and technical education.



390 MATHEMATICS



243, 244. Intermediate Calculus and Analysis. (3:3:0 ea.) Prerequisite: Math.
142 or consent of department.
Multidimensional calculus.

291, 292. Honors Seminar in Mathematics. (1:1:0 ea.)

Seminar in structure of mathematics. Primarily for freshman and
sophomore mathematics majors. Open to other interested students.

300. History of Mathematics. (3:3:0) Home Study also. Prerequisite: Math.
112 or 301.

The development of mathematics, with emphasis on the underlying prin-
ciples and motivations.

301. Foundations of Algebra. (3:3:0) Prerequisites: Math. 106, 111, or 305.

Sets; logic; basic number systems. Required of prospective secondary
teachers.

302. Foundations of Geometry. (3:3:0) Prerequisite: Math. 112, 141, or 301.

The logical structure of Euclidean and non-Euclidean geometries. Re-
quired of prospective secondary teachers.

305. Basic Concepts of Mathematics, (3:3:0)

Designed to develop understanding of the basic structure of mathematics.
Required of and restricted to prospective elementary teachers.

306. Concepts of Mathematics. (3:3:0) Prerequisite: Math. 305.

Modular arithmetic; real numbers; complex numbers; relations and
functions; informal geometry. For elementary teachers.

307. Mathematics and the Humanities. (3:3:0) (G-ML)

Elementary ideas in contemporary mathematics for non-physical science
majors.

315. Methods of Advanced Calculus. (3:3:0) (m) Prerequisite: Math. 214.

Topics from partial differentiation, multiple integration, infinite series,
uniform convergence. Primarily for engineers and science majors.

321. Applied Ordinary Differential Equations. (3:3:0) Home Study also. Pre-
requisite: Math. 214.

Ordinary differential equations with applications; Fourier series; Laplace
transforms. Primarily for engineers and science majors.

322. Topics in Applied Mathematics. (3:3:0) Home Study also. Prerequisite:
Math. 214.

Linear algebra, vector calculus, and Fourier analysis. For engineers and
science majors.

323. Applied Partial Differential Equations. (3:3:0) Home Study also. Prerequi-
site: Math. 321.

Boundary value problems; transform methods; Fourier series; Bessel
functions; Legendre polynomials. Primarily for engineers and science
majors.

332. Introduction to Complex Analysis. (3:3:0) Prerequisite: Math. 214 or 244.
Complex algebra; analytic functions; integration in the complex plane;
infinite series; theory of residues; conformal mapping.

371, 372. Abstract Algebra. (3:3:0 ea.) Prerequisite: Math. 142, 214, or 111
and 301.

Preliminary examination of algebraic systems: groups, rings, fields, vector
spaces, linear transformations, matrices, etc.

385. Linear Algebra. (3:3:0) Prerequisite: Math. Ill or 301.

Vectors and matrices; linear equations; determinants; characteristic
values; linear operators; quadratic forms; etc.



MATHEMATICS 391



387. Theory of Numbers. (3:3:0) Prerequisite: Math. Ill or 301.

Foundations of number theory; congruences; residues; reciprocity law;
Diophantine equations.

411. Numerical Methods. (3:3:0) Prerequisites: Comput. Sci. 130; Math. 214
or 244. Recommended: Math. 322 or 372 or 385.

Interpolation; approximation; differentiation; integration; ordinary differ-
ential equations; and systems of equations, both linear and nonlinear.

434. Introduction to Ordinary Differential Equations. (3:3:0) Home Study also.
Prerequisite: Math. 214 or 244.

Methods and theory of ordinary differential equations.

436. Introduction to Partial Differential Equations. (3:3:0) Prerequisite: Math.
321 or 434.

Methods for solving the wave, heat, and Laplace equations; eigenvalue
problems and Fourier series.

451. Modern Geometry I. (3:3:0) Prerequisite: Math. 301 or 371.

Synthetic and analytic projective geometry; affine and Euclidean geom-
etry. Geometry by invariants of groups of transformations.

452. Modern Geometry II. (3:3:0) Prerequisite: Math. 451.

Relationships of geometry to algebra, supplemental design, and combina-
torial mathematics.

495R. Readings in Mathematics. (1-2:0:1-3 ea.) Prerequisite: consent of in-
structor.

Directed readings beyond the scope of usual undergraduate courses. Of-
fered on demand.

501. Real Numbers. (3:3:0) Prerequisite: Math. 371. Recommended: Math. 451.

Extensive examination of various Eixiomatic descriptions of the real num-
bers and the interrelationships among these descriptions. Offered on de-
mand.

502. Set Theory. (3:3:0) Prerequisite: Math. 371.

Zermelo-Fraenkel axioms for set theory; the axiom of choice; ordinal and
cardinal numbers; algebra of sets. Offered on demand.

508. Mathematical Logic. (3:3:0) Prerequisite: Math. 371 or 541.

Prepositional and first-order predicate calculi; set theories; well-ordering;
transfinite induction.

512. Introduction to Numerical Analysis. (3:3:0) Prerequisite: Math. 411.
Theory of constructive methods in mathematical analysis.

513R. Advanced Topics in Applied Mathematics. (3:3:0 ea.) Prerequisite: con-
sent of instructor.
Offered on demand.

541, 542. Introduction to Real Analysis. (3:3:0 ea.) Prerequisite: Math. 244
or 315.

A rigorous treatment of continuity, differentiability, integration of func-
tions of real variables, and infinite series.

551, 552. Introduction to Topology. (3:3:0 ea.) Prerequisite: completion of or
concurrent registration in Math. 541.

Axiomatic treatment of linearly ordered spaces, metric spaces, arcs, and
Jordan curves; types of connectedness.

585. Matrix Analysis. (3:3:0) Prerequisite: Math. 322, 372, or 385.

Characteristic values, canonical forms, and functions of matrices, with ap-
plications.

629. Teaching Mathematics in Secondary Schools. (3:3:0)
Offered on demand.



392 MATHEMATICS



631, 632. Complex Analysis. (3:3:0 ea.) Prerequisites: Math. 332, 542.
Offered 1972-73 and alternate years.

634, 635. Theory of Ordinary Differential Equations. (3:3:0 ea.) Prerequisites:

Math. 434, 512.

Offered 1973-74 and alternate years.

641, 642. Functions of a Real Variable. (3:3:0 ea.) Prerequisite: Math. 542.
Offered 1973-74 and alternate years.

643R. Special Topics in Analysis. (3:3:0 ea.) Prerequisites: Math. 541, 542.

Topics selected from continued fractions, stochastic processes, generalized
functions, etc.

645. Tensor Analysis. (3:3:0) Prerequisite: Math. 244 or 542.
Offered on demand.

647, 648. Theory of Partial Differential Equations. (3:3:0 ea.) Prerequisites:

Math. 436, 542.

Offered 1972-73 and alternate years.

651, 652. General Topology I, II. (3:3:0 ea.) Prerequisite: consent of instructor.

653R. Special Topics in Geometry. (3:3:0 ea.) Prerequisites: Math. 372, 452.

Topics from n-dimensional projective and algebraic geometry, founda-
tions, transformations, curves and surfaces, and sheaf theory.

655R. Advanced Special Topics in Topology. (3:3:0 ea.) Prerequisite: consent of
instructor.

Offered on demand.

661, 662. Functional Analysis. (3:3:0 ea.) Prerequisite: Math. 632 or 642.
Offered on demand.

671, 672. Modern Algebra. (3:3:0 ea.) Prerequisites: Math. 371, 372.
Offered 1973-74 and alternate years.

675R. Special Topics in Algebra. (3:3:0 ea.) Prerequisite: Math. 671.

Group theory; commutative algebra; homological algebra; ring theory;
algebraic number theory.

681. Linear Algebra. (3:3:0) Prerequisites: Math. 371, 372.
Offered 1972-73 and alternate years.

695. Readings in Mathematics. (1-2:1-2:0)
Offered on demand.

699. Thesis for Master's Degree. (6-9:Arr.:Arr.)



MECHANICAL ENGINEERING SCIENCE 393



MechonicQ
Engineering




Professors: Anderson, Cannon, Free, Heaton, Polve, Simonsen (Chairman, 223B

FELB), Ulrich, Warner, Wille.
Associate Professor: Paxson.
Assistant Professor: Chase.

The Mechanical Engineering Science Department offers a professional engineering
program at the bachelor, master, and doctoral levels. The curriculum is fully
accredited by the Engineers' Council for Professional Development (ECPD).

Mechanical engineering is a creative branch of applied science that deals with
the analysis, design, development, fabrication, and application of products that
are of a predominately mechanical nature. Various subdivisions of mechanical
engineering are described below in the section entitled "Specialized Options."

The training program at BYU which leads to a degree in mechanical engineer-
ing is built upon a sound basis of mathematics, physics, and chemistry. The
engineering classroom and laboratory course work is taught by a faculty with
extensive academic and industrial experience. The technical program is supple-
mented by a well-balanced program of social sciences, religion, biological sciences,
and humanities. The professional nature of this training program enables the
graduate to be immediately productive upon graduation as well as to keep up
with new technological developments.

Mechanical engineering by its very nature includes many varieties of special-
ization. All students are provided with a central core of engineering fundamentals.
By proper selection of elective courses, a student can increase his depth in such
specialized areas as (1) aerospace, (2) automatic controls and systems analysis,
(3) bioengineering, (4) manufacturing and industrial engineering, (5) materials
and metallurgy, (6) mechanical design, (7) nuclear engineering, (8) solid
mechsinics, (9) thermoscience, and (10) vibration and dynamics. Each student
is assigned an adviser, who works with him in developing his individual program.

Students who are inclined toward more routine technical work should consult
the offerings of the College of Industrial and Technical Education.

Recommend High School Preparation

Special recommendations for incoming engineering students are contained in the
College of Physical and Engineering Sciences section of this catalog. A qualified
student who has sufficient high school preparation can complete the Bachelor of
Science degree program in four academic years. This time can be reduced by
attending school during the Spring and Summer terms. However, the degrees
offered by the department are awarded for competence level attained rather
than for a fixed number of years' attendance. Therefore, students with insuffi-
cient high school preparation may require additional classes to complete the
degree requirements, whereas those with more than adequate preparation can re-
duce the number of classes normally required.

Civil Engineering 101 (Introduction to Engineering Graphics) and Math. Ill
(College Algebra and Trigonometry) are prerequisites to the engineering program.
Students who pass placement tests given prior to registration will be excused



394 MECHANICAL ENGINEERING SOENCE



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MECHANICAL ENGINEERING SCIENCE 395



from taking these classes. Students who have sufficient preparation can also re-
ceive credit for History 170 and Health 130 — both required classes — by taking
special examinations.

Grade Requirements

To receive a bachelor's degree in mechanical engineering science, a student must
complete courses satisfying University general education requirements and
departmental requirements with a cumulative grade-point average of at least
2.00 (C). A maximum of 9 hours of D credit may be applied toward fulfilling
departmental requirements.

The graduate school requirement of a minimum 3.00 grade-point average
applies to all graduate degree programs. A minimum GPA of 2.50 is required in
the last 60 hours of course work prior to taking courses for graduate credit.
Students pursuing the integrated bachelor's-master's program for the Master of
Engineering degree should take special note of this, since they usually need to
apply for graduation admission during the junior year.

Suggested Course Sequences

Course sequences are outlined below for both the combined Bachelor of Science-
Master of Engineering program and for the Bachelor of Science only program.

The combined program is the generally recommended path leading to a pro-
fessional career in engineering practice. The B.S. program is designed for careers
in such fields as law, medicine, sales work, or other employment requiring less
engineering training.

Sequences for the combined five-year program and for the four-year program
are outlined by year and are also shown in flow charts with lines indicating
prerequisites. The prerequisite lines indicate how courses build upon each other.
In addition, a three-year B.S. program is outlined by year to show how the total
time may be shortened by attending school during the Spring and Summer
terms. The combined B.S. and M.E. program can, in a similar fashion, be com-
pleted in four years.

Combined B.S. and M.E. Degree Five- Year Program



First Year F

Mech. Eng. 101, 151 2

Civ. Eng. 102

Math. 112, 113 4

Physics 121, 122 3

Engl. Ill 3

♦Health 130 2

*Hist. 170

Relig. 121, 122 2

P.E. i

Dev. Assy. i



W

2
2
4
3



Total hours


17


17


Second Year


F


W


Mech. Eng. 201, 351


2


3


Civ. Eng. 201




2


Chem. 105, 106


4


4


Math. 214, 321


3


3


Physics 221


3




Physics 214


1




Stat. 332




2


Religion


2


2


P.E.


1


1


Dev. Assy.


i


i



Third Year

Mech. Eng. 321, 322

Mech. Eng. 363

Civ. Eng. 303, 304

Elec. Eng. 301

Math. 322

Engl. 316

Gen. ed. electives

Religion

Dev. Assy.

Total hours

Fourth Year

Mech. Eng. 412, 510
Mech. Eng. 534, 540
Mech. Eng. 431, 454
Elec. Eng. 302, 304
Elec. Eng. 303, 305
Math. 323
Gen. ed. electives
Dev. Assy.

Total hours



F

31

3i

3

2

1



W

4

3
2
3

2
2



17J 16i



W

31
31
3
2

1
3



165 16i



Total hours



16 17



396 MECHANICAL ENGINEERING SCIENCE



Fifth Year


F


W


Civ. Eng. 471




3


Mech. Eng. 471, 698


3


3


Gen. ed. electives


4


2


Mech. Eng. 591


h











Tech. electives


9


8


Total hours


16J


16



B.S. Degree Four-Year Program

First and second years are the same as combined B.S. and M. Eng. 5-year pro-
gram.

Third Year F W

Mech. Eng. 321, 322 3 4

Mech. Eng. 363 2

Civ. Eng. 303, 304 3 3

Elec. Eng. 301 2

Engl. 316 3

Gen. ed. electives 4 6

Religion 2 2

Dev. Assy. i i

Total hours 17* 171 Total hours 16i 171



Fourth Year


F


W


Mech. Eng. 412, 471


3i


3


Mech. Eng. 431, 454


3


3


Tech. electives


3h


6


Civ. Eng. 471




3


Elec. Eng. 302 or 304


2




Elec. Eng. 303 or 305


1




Gen. ed. electives


3


2


Dev. Assy.


h


i



B.S. Degree Three- Year Program

First Year F W Sp

Mech. Eng. 101, 151 2 2
Civ. Eng. 102, 201 2 2

Math. 112, 113, 214 4 4 3

Physics 121, 122 3 3

Engl. Ill 3

*Health 130 2
*Hist. 170 3

Gen. ed. elective 3

Relig. 121, 122 2 2
P.E. i h

Dev. Assy. I i

Total hours 17 17 8

Second Year F W Sp

Mech. Eng. 201 2

Mech. Eng. 321, 363 3 2

Civ. Eng. 303, 304 3 3

Chem. 105, 106 4 4

Math. 321 3

Stat. 332 2

Physics 221 3

Physics 214 1 Total hours

Engl. 316 3

*History 170 and Health 130 can be passed by examination.



Gen. ed. electives

Religion

P.E.

Dev. Assy.

Total hours

Third Year F

Mech. Eng. 412 3i
Mech. Eng. 322 4
Mech. Eng. 431,

454, 471 3

Mech. Eng. 351 3
Tech. electives
Civ. Eng. 471
Elec. Eng. 301. 302

or 304
Elec. Eng. 303

or 305
Gen. ed. electives 4