Natural Science Majors
■Applied Mathematical Sciences Major
Mathematics has been a central feature of humanity’s intellectual achievements over the past several centuries. Its role in the physical sciences and
engineering is well established and continues to aid in their development. Mathematics is also becoming increasingly important in the social and life
sciences with a wide range of new applications requiring sophisticated mathematical techniques. Thus, the field of applied mathematical sciences is
undergoing remarkable growth.
UC Merced offers an undergraduate major leading to a B.S. degree in the Applied Mathematical Sciences. This educational experience provides
students with knowledge of the foundations of mathematics and the skills needed to apply mathematics to real-world phenomena in the social
sciences, natural sciences and engineering. The curriculum is composed of courses in the fundamentals while allowing for building expertise in an
application area through the emphasis tracks. There is a core set of courses all mathematical sciences students take. Beyond these classes, students
complete an emphasis track consisting of courses in other fields. Some examples of emphasis tracks include physics, computational biology,
economics, computer science and engineering, and engineering mechanics. New emphasis tracks will be added alongside new programs developing
at UC Merced. Students may also design their own emphasis track with the approval of the faculty program leads for the Applied Mathematical
Sciences major.
A degree in applied mathematical sciences opens the door to a wide variety of careers. Employers understand that a degree in mathematics means a
student has been trained well in analytical reasoning and problem solving. Moreover, applied mathematical sciences majors with skills in scientific
computing have the additional leverage of substantial computing experience. The market for applied mathematicians has usually been good,
especially for those who can relate their mathematics to real world problems. In particular, applied mathematics majors familiar with concepts in
management, biology, engineering, economics or the environmental sciences among others are well suited for many specialized positions. In
addition, the breadth and rigor of this program provide an excellent preparation to teach mathematics at the elementary or high school levels.
Requirements for the Applied Mathematical Sciences Major (MATH)
Students majoring in Applied Mathematical Sciences must adhere to all UC Merced and School of Natural Sciences requirements. For the
Math/Science Preparatory Curricula, students majoring in Applied Mathematical Sciences must take:
MATH 021: Calculus I for Physical Sciences and Engineering. . . 4 units
MATH 032: Probability & Statistics . . . . . . . . . . . . . . . . . . . . . . . 4 units
PHYS 008: Introductory Physics I. . . . . . . . . . . . . . . . . . . . . . . . . 4 units
CSE 020: Introduction to Computing . . . . . . . . . . . . . . . . . . . . . 4 units
CHEM 002: General Chemistry I. . . . . . . . . . . . . . . . . . . . . . . . . 4 units
The additional requirements that must be met to obtain the B.S. degree in the Applied Mathematical Sciences at UC Merced are:
Applied Mathematical Sciences Requirements (62-64 units): The Applied Mathematical Sciences major consists of 16 courses (5 or 6 lower division
and 10 or 11 upper division, depending on the emphasis track chosen) designed to give all students a common foundation of core knowledge specific
to the discipline, plus breadth in an application area.
LOWER DIVISION COURSES [20 UNITS]
BIO 001: Contemporary Biology, ESS 001: Introduction to Earth Systems
Science or ESS 005: Introduction to Biological Earth Systems*. . . 4 units
MATH 022: Calculus II for Physical Sciences and Engineering. . . 4 units
MATH 023: Vector Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 units
MATH 024: Linear Algebra and Differential Equations. . . . . . . . . 4 units
PHYS 009: Introductory Physics II.. . . . . . . . . . . . . . . . . . . . . . . . 4 units
* For the Computational Biology emphasis track listed below, students must take BIO 001 and BIO 001L: Contemporary Biology Lab
UPPER DIVISION COURSES [24 UNITS]
MATH 122: Complex Variables and Applications. . . . . . . . . . . . 4 units
MATH 125: Intermediate Differential Equations . . . . . . . . . . . . . 4 units
MATH 126: Partial Differential Equations . . . . . . . . . . . . . . . . . . 4 units
MATH 131: Numerical Analysis I. . . . . . . . . . . . . . . . . . . . . . . . . 4 units
MATH 132: Numerical Analysis II. . . . . . . . . . . . . . . . . . . . . . . . . 4 units
MATH 141: Linear Analysis I. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 units
EMPHASIS TRACKS [18-20 UNITS]
The student must complete at least 18 units of approved course work from other programs toward the completion of an emphasis track. At least 10 of
these 18 units must be upper division courses. Some examples of emphasis tracks include physics, computational biology, economics, computer
science, and engineering. These examples appear in the sample course plans below. More application themes will become available as new programs
on campus develop. Students may design their own emphasis track with approval from the faculty program leads for the Applied Mathematical
Sciences major.
Additional Requirements for Physics Emphasis Track
PHYS 010: Introductory Physics III. . . . . . . . . . . . . . . . . . . . . . . . 4 units
PHYS 105: Analytical Mechanics Core. . . . . . . . . . . . . . . . . . . . . 4 units
PHYS 110: Electrodynamics Core. . . . . . . . . . . . . . . . . . . . . . . . . 4 units
PHYS 112: Statistical Mechanics Core. . . . . . . . . . . . . . . . . . . . . 4 units
PHYS 137: Quantum Mechanics Core. . . . . . . . . . . . . . . . . . . . . 4 units
Additional Requirements for Computational Biology Emphasis Track
BIO 002: Introduction to Molecular Biology. . . . . . . . . . . . . . . . . . 4 units
BIO 175: Biostatistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 units
BIO 180: Mathematical Modeling for Biology . . . . . . . . . . . . . . . 4 units
BIO 181: Survey of Computational Biology. . . . . . . . . . . . . . . . . 4 units
BIO 182: Bioinformatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 units
Additional Requirements for Economics Emphasis Track
ECON 001: Introduction to Economics . . . . . . . . . . . . . . . . . . . . 4 units
ECON 100: Intermediate Microeconomic Theory. . . . . . . . . . . . . 4 units
ECON 101: Intermediate Macroeconomic Theory . . . . . . . . . . . . 4 units
ECON 130: Econometrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 units
One additional upper division ECON course . . . . . . . . . . . . . . . . 4 units
Additional Requirements for Computer Science Emphasis Track
CSE 030: Introduction to Computer Science and Engineering I .. 4 units
CSE 031: Introduction to Computer Science and Engineering II.. 4 units
CSE 100: Algorithm Design and Analysis. . . . . . . . . . . . . . . . . . . 4 units
CSE 111: Database Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 units
CSE 160: Networking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 units
Additional Requirements for Engineering Emphasis Track
ENGR 057: Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 units
ENGR 120: Fluid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 units
ENGR 130: Thermodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 units
ENGR 151: Strength of Materials . . . . . . . . . . . . . . . . . . . . . . . . 4 units
ME 135 Finite Element Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . 3 units
Transfer Students
Transfer students who wish to major in Applied Mathematical Sciences should complete two semesters of calculus of a single variable, vector
calculus, linear algebra and differential equations. In addition, transfer students should complete one semester of general chemistry with laboratory
and two semesters of calculus-based physics with laboratory. Students should consult the online student transfer information system at
www.assist.org. Students should also consult the Information for Prospective Students link on the School of Natural Sciences web site
naturalsciences.ucmerced.edu for more information.
Program Learning Outcomes for the Applied Mathematical Sciences Major
The over-arching goal of the Applied Mathematical Sciences program is to build a community of life-long learners that use the analytical and
computational tools of mathematics to solve real world problems.
Upon graduating, we expect students completing the Applied Mathematical Sciences major to have become effective problem solvers, meaning that
student will be able to
1.
2.
3.
4.
5.
Solve mathematical problems using analytical methods.
Solve mathematical problems using computational methods.
Recognize the relationships between different areas of mathematics and the connections between mathematics and other disciplines.
Give clear and organized written and verbal explanations of mathematical ideas to a variety of audiences.
Model real-world problems mathematically and analyze those models using their mastery of the core concepts.
SAMPLE PLAN OF STUDY FOR APPLIED MATHEMATICAL SCIENCES DEGREE–PHYSICS EMPHASIS
SEMESTER 1
MATH 021 Calculus I for Physical Sciences and Engineering 4
PHYS 008 Introductory Physics I 4
CORE 001 The World at Home 4
CSE 020 Introduction to Computing I 2
Freshman Seminar* 1
Semester Units 15
SEMESTER 2
MATH 022 Calculus II for Physical Sciences and Engineering 4
PHYS 009 Introductory Physics II 4
CHEM 002 General Chemistry I 4
WRI 010 College Reading and Composition 4
Semester Units 16
SEMESTER 3
MATH 023 Vector Calculus 4
MATH 032 Probability and Statistics 4
PHYS 010 Introductory Physics III 4
General Education Elective (Arts/Humanities) 4
Semester Units 16
SEMESTER 4
MATH 024 Linear Algebra and Differential Equations 4
PHYS 105 Analytic Mechanics Core 4
BIO 001 Contemporary Biology** 4
MATH 091 Topics in Applied Mathematics* 1
Free Elective 3
Semester Units 16
SEMESTER 5
MATH 125 Intermediate Differential Equations 4
MATH 131 Numerical Analysis I 4
PHYS 110 Electrodynamics Core 4
General Education (Social/Cognitive Sciences) 4
Semester Units 16
SEMESTER 6
MATH 122 Complex Variables and Applications 4
MATH 132 Numerical Analysis II 4
CORE 100 The World at Home 4
Free Elective 3
Semester Units 15
SEMESTER 7
MATH 141 Linear Analysis I 4
PHYS 137 Quantum Mechanics Core 4
General Education (communication) 4
General Education Elective 4
Semester Units 16
SEMESTER 8
MATH 126 Partial Differential Equations 4
PHYS 112 Statistical Mechanics Core 4
Upper division sciences/engineering elective 4
Free Elective 3
Semester Units 15
Total Program Units 125
* Freshman Seminar and Math 091 are optional courses; they are not required for Applied Math majors.
** or ESS 001 Introduction to Earth Systems Science or ESS 005 Introduction to Biological Earth Systems.
The four-year plans presented in this catalog demonstrate the recommended sequencing and timing of the required and elective components within each major. In many cases, a student’s
academic background will require variations in the timing of the coursework listed in the plan. All students are expected to work with their academic advisor to find their best pathway through
the degree requirements of their chosen program.
PLAN OF STUDY FOR APPLIED MATHEMATICAL SCIENCES DEGREE–COMPUTATIONAL BIOLOGY EMPHASIS
SEMESTER 1
MATH 021 Calculus I for Physical Sciences and Engineering 4
BIO 001 Contemporary Biology 4
CORE 001 The World at Home 4
CSE 020 Introduction to Computing I 2
Freshman Seminar* 1
Semester Units 15
SEMESTER 2
MATH 022 Calculus II Physical Sciences and Engineering 4
PHYS 008 Introductory Physics I 4
CHEM 002 General Chemistry I 4
WRI 010 College Reading and Composition 4
Semester Units 16
SEMESTER 3
MATH 023 Vector Calculus 4
CHEM 8 Principles of Organic Chemistry 4
BIO 002 Introduction to Molecular Biology 4
General Education Elective (Humanities and Arts) 4
Semester Units 16
SEMESTER 4
MATH 024 Linear Algebra and Differential Equations 4
MATH 032 Probability and Statistics 4
BIO 180 Mathematical Modeling for Biology 4
PHYS 009 Introductory Physics II 4
MATH 091 Topics in Applied Mathematics* 1
Semester Units 17
SEMESTER 5
BIO 175 Biostatistics 4
MATH 125 Intermediate Differential Equations 4
MATH 131 Numerical Analysis I 4
General Education (Social and Cognitive Sciences) 4
Semester Units 16
SEMESTER 6
MATH 122 Complex Variables and Applications 4
MATH 126 Partial Differential Equations 4
BIO 181 Survey of Computational Biology 4
Free Elective 3
Semester Units 15
SEMESTER 7
MATH 141 Linear Analysis I 4
BIO 182 Bioinformatics 4
General Education (communication) 4
General Education Elective 4
Semester Units 16
SEMESTER 8
MATH 132 Numerical Analysis II 4
CORE 100 The World at Home 4
Upper division Science/Engineering Elective 4
Free Elective 3
Semester Units 15
Total Program Units 126
* Freshman Seminar and Math 091 are optional courses; they are not required for Applied Math majors.
The four-year plans presented in this catalog demonstrate the recommended sequencing and timing of the required and elective components within each major. In many cases, a student’s
academic background will require variations in the timing of the coursework listed in the plan. All students are expected to work with their academic advisor to find their best pathway through
the degree requirements of their chosen program.
SAMPLE PLAN OF STUDY FOR APPLIED MATHEMATICAL SCIENCES DEGREE–ECONOMICS EMPHASIS TRACK
SEMESTER 1
MATH 021 Calculus I for Physical Sciences and Engineering 4
PHYS 008 Introductory Physics I 4
CORE 001 The World at Home 4
CSE 020 Introduction to Computing I 2
Freshman Seminar* 1
Semester Units 15
SEMESTER 2
MATH 022 Calculus II Physical Sciences and Engineering 4
PHYS 009 Introductory Physics II 4
CHEM 002 General Chemistry I 4
WRI 010 College Reading and Composition 4
Semester Units 16
SEMESTER 3
MATH 023 Multi-Variable Calculus 4
ECON 001 Introduction to Economics** 4
BIO 001 Contemporary Biology*** 4
General Education Elective (Humanities and Arts) 4
Semester Units 16
SEMESTER 4
MATH 024 Linear Algebra and Differential Equations 4
MATH 032 Probability and Statistics 4
MATH 091 Topics in Applied Mathematics* 1
ECON 010 Statistical Inference 4
Free Elective 3
Semester Units 16
SEMESTER 5
MATH 125 Intermediate Differential Equations 4
ECON 100 Intermediate Microeconomic Theory 4
MATH 131 Numerical Analysis I 4
General Education (Social and Cognitive Sciences) 4
Semester Units 16
SEMESTER 6
MATH 122 Complex Variables and Applications 4
MATH 126 Partial Differential Equations 4
CORE 100 The World at Home 4
Free Elective 3
Semester Units 15
SEMESTER 7
ECON 130 Econometrics 4
MATH 141 Linear Analysis I 4
General Education (communication) 4
General Education Elective 4
Semester Units 16
SEMESTER 8
MATH 132 Numerical Analysis II 4
ECON 101 Intermediate Macroeconomic Theory 4
Upper division Science/Engineering Elective 4
Upper Division Economics course 4
Semester Units 16
Total Program Units 126
* Freshman Seminar and Math 091 are optional courses; they are not required for Applied Math majors.
** ECON 001 can be used to satisfy a Social and Cognitive Sciences General Education Requirement.
*** Or ESS 001 Introduction to Earth Systems Science or ESS 005 Introduction to Biological Earth Systems.
The four-year plans presented in this catalog demonstrate the recommended sequencing and timing of the required and elective components within each major. In many cases, a student’s
academic background will require variations in the timing of the coursework listed in the plan. All students are expected to work with their academic advisor to find their best pathway through
the degree requirements of their chosen program.
SAMPLE PLAN OF STUDY FOR APPLIED MATHEMATICAL SCIENCES DEGREE–COMPUTER SCIENCE EMPHASIS TRACK
SEMESTER 1
MATH 021 Calculus I for Physical Sciences and Engineering 4
PHYS 008 Introductory Physics I 4
CORE 001 The World at Home 4
CSE 020 Introduction to Computing I 2
Freshman Seminar* 1
Semester Units 15
SEMESTER 2
MATH 022 Calculus II Physical Sciences and Engineering 4
PHYS 009 Introductory Physics II 4
CHEM 002 General Chemistry I 4
CSE 021 Introduction to Computing II 2
Free Elective 3
Semester Units 17
SEMESTER 3
MATH 023 Multi-Variable Calculus 4
CSE 030 Introduction to Computer Science And
Engineering I 4
BIO 001 Contemporary Biology** 4
General Education Elective (Arts/Humanities) 4
Semester Units 16
SEMESTER 4
MATH 024 Linear Algebra and Differential Equations 4
CSE 031 Introduction to Computer Science And
Engineering II 4
MATH 032 Probability and Statistics 4
MATH 091 Topics in Applied Mathematics* 1
WRI 010 College Reading and Composition 4
Semester Units 17
SEMESTER 5
MATH 125 Intermediate Differential Equations 4
CSE 100 Algorithm Design and Analysis 4
MATH 131 Numerical Analysis I 4
General Education (Social and Cognitive Sciences) 4
Semester Units 16
SEMESTER 6
MATH 122 Complex Variables and Applications 4
MATH 132 Numerical Analysis II 4
CORE 100 The World at Home 4
Free Elective 3
Semester Units 15
SEMESTER 7
CSE 160 Networking 4
MATH 141 Linear Analysis I 4
General Education Elective (communication) 4
General Education Elective 4
Semester Units 16
SEMESTER 8
MATH 126 Partial Differential Equations 4
CSE 111 Database Systems 4
Upper division Science/Engineering Elective 4
Free Elective 3
Semester Units 15
Total Program Units 127
* Freshman Seminar and Math 091 are optional courses; they are not required for Applied Math majors.
** Or ESS 001 Introduction to Earth Systems Science or ESS 005 Introduction to Biological Earth Systems.
The four-year plans presented in this catalog demonstrate the recommended sequencing and timing of the required and elective components within each major. In many cases, a student’s
academic background will require variations in the timing of the coursework listed in the plan. All students are expected to work with their academic advisor to find their best pathway through
the degree requirements of their chosen program.
SAMPLE PLAN OF STUDY FOR APPLIED MATHEMATICAL SCIENCES DEGREE–ENGINEERING EMPHASIS TRACK
SEMESTER 1
MATH 021 Calculus I for Physical Sciences and Engineering 4
PHYS 008 Introductory Physics I 4
CORE 001 The World at Home 4
CSE 020 Introduction to Computing I 2
Freshman Seminar* 1
Semester Units 15
SEMESTER 2
MATH 022 Calculus II Physical Sciences and Engineering 4
PHYS 009 Introductory Physics II 4
CHEM 002 General Chemistry I 4
WRI 010 College Reading and Composition 4
Semester Units 16
SEMESTER 3
MATH 023 Vector Calculus 4
MATH 032 Probability and Statistics 4
General Education Elective (Arts/Humanities) 4
Free Elective 3
Semester Units 15
SEMESTER 4
MATH 024 Linear Algebra and Differential Equations 4
BIO 001 Contemporary Biology** 4
ENGR 057 Dynamics 4
MATH 091 Topics in Applied Mathematics* 1
Free Elective 3
Semester Units 16
SEMESTER 5
MATH 125 Intermediate Differential Equations 4
MATH 131 Numerical Analysis I 4
ENGR 151 Strength of Materials 4
General Education (Social and Cognitive Sciences) 4
Semester Units 16
SEMESTER 6
MATH 122 Complex Variables and Applications 4
MATH 132 Numerical Analysis II 4
CORE 100 The World at Home 4
ENGR 130 Thermodynamics 3
Semester Units 15
SEMESTER 7
MATH 141 Linear Analysis I 4
ME 135 Finite Element Analysis 3
General Education Elective (communication) 4
General Education Elective 4
Semester Units 15
SEMESTER 8
MATH 126 Partial Differential Equations 4
ENGR 120 Fluid Mechanics 4
Upper division Science/Engineering Elective 4
Free Elective 3
Semester Units 15
Total Program Units 123
* Freshman Seminar and Math 091 are optional courses; they are not required for Applied Math majors.
** Or ESS 001 Introduction to Earth Systems Science or ESS 005 Introduction to Biological Earth Systems.
The four-year plans presented in this catalog demonstrate the recommended sequencing and timing of the required and elective components within each major. In many cases, a student’s
academic background will require variations in the timing of the coursework listed in the plan. All students are expected to work with their academic advisor to find their best pathway through
the degree requirements of their chosen program.