# Mathematics B.A./B.S.

The degree program requires a basic core of courses (44 credits) and elective courses (18-21 credits). This structure gives flexibility to the program that allows students to pursue special areas of interest in mathematics. The program is designed to provide a foundation for more advanced work and/or a basis for employment in business, government, industry, or secondary education.

## Requirements

In addition to meeting the general University degree requirements, the major in mathematics must complete the following requirements:

### Courses

Mth 251 | Calculus I | 4 |

Mth 252 | Calculus II | 4 |

Mth 253 | Calculus III | 4 |

Mth 261 | Introduction to Linear Algebra | 4 |

Mth 254 | Calculus IV | 4 |

Mth 255 | Calculus V | 4 |

Mth 256 | Applied Ordinary Differential Equations | 4 |

Mth 271 | Mathematical Computing | 4 |

or | ||

CS 161 | Introduction to Programming and Problem-Solving | 4 |

Mth 311 | Introduction to Mathematical Analysis I | 4 |

Mth 312 | Introduction to Mathematical Analysis II | 4 |

Mth 344 | Introduction to Group Theory and Applications | 4 |

### Additional Requirements chosen from Approved List of courses-sequences

Mth/Stat (one) | Approved two-term 400-level Mth or Stat sequence | 6 |

Mth/Stat (two) | Approved 400-level Mth or Stat courses | 6-7 |

Mth/Stat (two) | Approved 300- or 400-level Mth or Stat courses | 6-8 |

**Total Credit Hours: 62-65**

### Approved electives are:

Mth 300 | Introduction to Mathematical Reasoning | 4 |

Mth 313 | Advanced Multivariate Calculus | 4 |

Mth 322 | Applied Partial Differential Equations | 4 |

Mth 324 | Vector Analysis | 4 |

Mth 338 | Modern College Geometry | 4 |

Mth 343 | Applied Linear Algebra | 4 |

Mth 345 | Introduction to Ring and Field Theory | 4 |

Mth 346 | Number Theory | 4 |

Mth 356 | Discrete Mathematics | 4 |

Mth 371 | Large-Scale Data Algorithms | 4 |

Mth 411 | Introduction to Real Analysis I | 3 |

Mth 412 | Introduction to Real Analysis II | 3 |

Mth 413 | Introduction to Real Analysis III | 3 |

Mth 420 | Introduction to Complexity Theory | 3 |

Mth 421 | Theory of Ordinary Differential Equations I | 3 |

Mth 422 | Theory of Ordinary Differential Equations II | 3 |

Mth 423 | Theory of Ordinary Differential Equations III | 3 |

Mth 424 | Elementary Differential Geometry I | 3 |

Mth 425 | Elementary Differential Geometry II | 3 |

Mth 427 | Partial Differential Equations I | 3 |

Mth 428 | Partial Differential Equations II | 3 |

Mth 430 | Topics in Mathematical Modeling | 3 |

Mth 431 | Topics in Geometry I | 3 |

Mth 432 | Topics in Geometry II | 3 |

Mth 433 | Topics in Geometry III | 3 |

Mth 434 | Set Theory and Topology I | 3 |

Mth 435 | Set Theory and Topology II | 3 |

Mth 436 | Set Theory and Topology III | 3 |

Mth 441 | Introduction to Abstract Algebra I | 3 |

Mth 442 | Introduction to Abstract Algebra II | 3 |

Mth 443 | Introduction to Abstract Algebra III | 3 |

Mth 444 | Advanced Linear/Multilinear Algebra I | 3 |

Mth 445 | Advanced Linear/Multilinear Algebra II | 3 |

Mth 449 | Topics in Advanced Number Theory | 3 |

Mth 451 | Numerical Calculus I | 3 |

Mth 452 | Numerical Calculus II | 3 |

Mth 453 | Numerical Calculus III | 3 |

Mth 456 | Topics in Combinatorics | 3 |

Mth 457 | The Mathematical Theory of Games I | 3 |

Mth 458 | The Mathematical Theory of Games II | 3 |

Mth 461 | Graph Theory I | 3 |

Mth 462 | Graph Theory II | 3 |

Mth 464 | Numerical Optimization I | 3 |

Mth 465 | Numerical Optimization II | 3 |

Mth 470 | Complex Analysis and Boundary Value Problems I | 3 |

Mth 471 | Complex Analysis and Boundary Value Problems II | 3 |

Mth 472 | Complex Analysis and Boundary Value Problems III | 3 |

Mth 477 | Mathematical Control Theory I | 3 |

Mth 478 | Mathematical Control Theory II | 3 |

Mth 481 | Topics in Probability for Mathematics Teachers | 3 |

Mth 482 | Topics in Statistics for Mathematics Teachers | 3 |

Mth 483 | Topics in Geometry for Mathematics Teachers | 3 |

Mth 484 | Topics in Algebra for Mathematics Teachers | 3 |

Mth 485 | Topics in Analysis for Mathematics Teachers | 3 |

Mth 486 | Topics in The History of Mathematics | 3 |

Mth 487 | Topics in Discrete Mathematics for Mathematics Teachers | 3 |

Mth 488 | Topics in Computing for Mathematics Teachers | 3 |

Stat 361 | Introduction to Statistical Methods | 4 |

Stat 363 | Statistical Computing and Data Visualization in R | 4 |

Stat 364 | Modern Regression Analysis | 4 |

Stat 387 | Introduction to Statistical Learning | 4 |

Stat 451 | Applied Statistics for Engineers and Scientists I | 4 |

Stat 452 | Applied Statistics for Engineers and Scientists II | 3 |

Stat 461 | Introduction to Mathematical Statistics I | 3 |

Stat 462 | Introduction to Mathematical Statistics II | 3 |

Stat 463 | Introduction to Mathematical Statistics III | 3 |

Stat 464 | Applied Regression Analysis | 3 |

Stat 465 | Experimental Design: Theory and Methods I | 3 |

Stat 466 | Experimental Design: Theory and Methods II | 3 |

Stat 467 | Applied Probability I | 3 |

Stat 468 | Applied Probability II | 3 |

Check with the department for the list of approved Mth or Stat sequences and for additional courses, including omnibus-numbered courses, which may be approved as electives.

All courses used to satisfy the mathematical major requirements, whether taken in the department or elsewhere, must be graded C-, P, or above, but no more than 4 courses graded P will count toward these requirements. Transfer students majoring in mathematics are required to take a minimum of 15 credits of PSU upper-division mathematics or statistics courses in residence.

## Mathematics B.A./B.S. Options

In addition to the specific required courses, the following options are intended to help the student plan a program of study with a specific goal or career in mind.

### Option I—Applied Mathematics

#### Recommended electives:

Mth 322 | Applied Partial Differential Equations | 4 |

Mth 343 | Applied Linear Algebra | 4 |

Mth 371 | Large-Scale Data Algorithms | 4 |

Mth 421 | Theory of Ordinary Differential Equations I | 3 |

Mth 422 | Theory of Ordinary Differential Equations II | 3 |

Mth 424 | Elementary Differential Geometry I | 3 |

Mth 425 | Elementary Differential Geometry II | 3 |

Mth 427 | Partial Differential Equations I | 3 |

Mth 428 | Partial Differential Equations II | 3 |

Mth 430 | Topics in Mathematical Modeling | 3 |

Mth 451 | Numerical Calculus I | 3 |

Mth 452 | Numerical Calculus II | 3 |

Mth 457 | The Mathematical Theory of Games I | 3 |

Mth 458 | The Mathematical Theory of Games II | 3 |

Mth 464 | Numerical Optimization I | 3 |

Mth 465 | Numerical Optimization II | 3 |

Mth 470 | Complex Analysis and Boundary Value Problems I | 3 |

Mth 477 | Mathematical Control Theory I | 3 |

Mth 478 | Mathematical Control Theory II | 3 |

### Option II—Graduate School Preparation

#### Recommended electives:

Mth 411 | Introduction to Real Analysis I | 3 |

Mth 412 | Introduction to Real Analysis II | 3 |

Mth 413 | Introduction to Real Analysis III | 3 |

Mth 434 | Set Theory and Topology I | 3 |

Mth 435 | Set Theory and Topology II | 3 |

Mth 436 | Set Theory and Topology III | 3 |

Mth 441 | Introduction to Abstract Algebra I | 3 |

Mth 442 | Introduction to Abstract Algebra II | 3 |

Mth 443 | Introduction to Abstract Algebra III | 3 |

### Option III—Statistics

#### Recommended electives:

Stat 361 | Introduction to Statistical Methods | 4 |

Stat 363 | Statistical Computing and Data Visualization in R | 4 |

Stat 364 | Modern Regression Analysis | 4 |

Stat 387 | Introduction to Statistical Learning | 4 |

Stat 461 | Introduction to Mathematical Statistics I | 3 |

Stat 462 | Introduction to Mathematical Statistics II | 3 |

Stat 463 | Introduction to Mathematical Statistics III | 3 |

Stat 464 | Applied Regression Analysis | 3 |

Stat 465 | Experimental Design: Theory and Methods I | 3 |

Stat 466 | Experimental Design: Theory and Methods II | 3 |

Stat 467 | Applied Probability I | 3 |

Stat 468 | Applied Probability II | 3 |

### Option IV—High School Teaching

#### Recommended electives:

Mth 338 | Modern College Geometry | 4 |

Mth 346 | Number Theory | 4 |

Mth 356 | Discrete Mathematics | 4 |

Mth 486 | Topics in The History of Mathematics | 3 |

Mth 488 | Topics in Computing for Mathematics Teachers | 3 |

Stat 461 | Introduction to Mathematical Statistics I | 3 |

Stat 462 | Introduction to Mathematical Statistics II | 3 |

See also the Mathematics Licensure section.

### Option V—Actuarial Science

#### Recommended electives:

Mth 271 | Mathematical Computing | 4 |

Mth 451 | Numerical Calculus I | 3 |

Mth 452 | Numerical Calculus II | 3 |

Stat 451 | Applied Statistics for Engineers and Scientists I | 4 |

Stat 461 | Introduction to Mathematical Statistics I | 3 |

Stat 462 | Introduction to Mathematical Statistics II | 3 |

Stat 463 | Introduction to Mathematical Statistics III | 3 |

Stat 464 | Applied Regression Analysis | 3 |

Stat 465 | Experimental Design: Theory and Methods I | 3 |

Stat 466 | Experimental Design: Theory and Methods II | 3 |

Stat 467 | Applied Probability I | 3 |

Stat 468 | Applied Probability II | 3 |

## Mathematics and Statistics Honors Track

The Honors Track in Mathematics and Statistics offers an opportunity for outstanding mathematics majors to engage in independent research under the supervision of a faculty member. Students who successfully complete the honors track will receive notice of this distinction on their academic transcripts and on their diplomas.

The requirements for admission to the Mathematics and Statistics Honors Track are:

- Completion of 12 credits in the Fariborz Maseeh Department of Mathematics and Statistics, 4 of which should be at a 300-level or above;
- A minimum cumulative GPA of 3.5 points and a minimum GPA of 3.67 points in the mathematics major;
- A complete application form submitted to the Fariborz Maseeh Department of Mathematics and Statistics no later than three quarters before graduation.

### Requirements

The Mathematics and Statistics Honors Track requirements for graduation are:

#### Courses

Mth 251 | Calculus I | 4 |

Mth 252 | Calculus II | 4 |

Mth 253 | Calculus III | 4 |

Mth 254 | Calculus IV | 4 |

Mth 255 | Calculus V | 4 |

Mth 261 | Introduction to Linear Algebra | 4 |

Mth 256 | Applied Ordinary Differential Equations | 4 |

Mth 311 | Introduction to Mathematical Analysis I | 4 |

Mth 312 | Introduction to Mathematical Analysis II | 4 |

Mth 344 | Introduction to Group Theory and Applications | 4 |

Mth 401 | Honors Project | 3 |

Mth 271 | Mathematical Computing | 4 |

or | ||

CS 161 | Introduction to Programming and Problem-Solving | 4 |

#### Additional Requirements chosen from Approved List of courses-sequences

Mth/Stat (two) | Approved 400-level sequences | 12 |

Mth/Stat (one) | Approved 300- or 400-level elective course | 3-4 |

The chair of the Fariborz Maseeh Department of Mathematics and Statistics, in consultation with faculty, will assign the students a faculty honors project adviser to guide their research. The research topic will be at a 400-level or above and will not have been discussed or presented in courses the students have taken. Concluding the work, the students will give an oral presentation of the honors project to faculty and students.

Students must have a cumulative GPA no lower than 3.5 points and a GPA no lower than 3.67 points in the major.

No mathematics or statistics courses taken under the undifferentiated grading option are acceptable towards fulfilling the requirements for the Mathematics and Statistics Honors Track. Transfer students majoring in mathematics are required to take a minimum of 15 credits of PSU upper-division mathematics or statistics courses in residence.

The chair and an undergraduate adviser will monitor the progress of the students accepted in the Mathematics and Statistics Honors Track. If this progress and/or performance are found to be unsatisfactory and if corrective actions cannot be identified, the students will be dropped from the Mathematics and Statistics Honors Track (the students may opt out to pursue a regular mathematics major or to select another major).

**University Honors College Students**

Students in the University Honors College majoring in mathematics have two options for completing their Honors thesis project:

**Option 1:** Apply to join the Mathematics Departmental Honors Track program, complete the required coursework, and register for Hon 403: Thesis Prospectus (4 credits) in the quarter immediately preceding the Mth 401: Honors Project (3 credits). During the thesis prospectus course students will work with their mathematics honors project adviser in the department of Mathematics and Statistics to identify a research question and topic, which they will then carry out during the quarter they are registered for Mth 401. University Honors College will accept the Mth 401 credits in lieu of additional Hon 403 thesis credits. The Mth 401 research project will fulfill the honors thesis requirement. (Students are permitted to register for Hon 403: Thesis Continuation credits if they would prefer additional support or credit hours.) Students are required to give an oral presentation of their completed research projects to faculty and students in the Mathematics and Statistics department as well as at the Honors Thesis symposium for University Honors College faculty and students. Students earn both Mathematics Departmental Honors and University Honors.

**Option 2:** University Honors College students who do not meet the minimum requirements or who choose not to join the Mathematics Departmental Honors Track program must still fulfill the requirements of two approved 400 level sequences in mathematics and/or statistics. They are then eligible to proceed with the math honors research project, taking Hon 403: Thesis Prospectus and then Mth 401: Honors Project under the supervision of a Mathematics and Statistics faculty adviser. Students earn University Honors but not Departmental Honors.