# Randolph Goldman PH.D.

##### College of Natural and Computational Sciences - Department of Mathematics

**Associate Professor of Mathematics**

**Department Chair**

**Education:**

- Ph.D., Logic and Methodology of Science, University of California at Berkeley
- M.A., Mathematics, University of California at Berkeley
- M.S., Computer Science, University of California at Santa Cruz,
- J.D., University of Hawaii at Manoa
- B.A., Mathematics, University of California at Berkeley

**Courses Taught:**

- MATH 1150 Pre-Calculus I and II Accelerated
- MATH 2214 Calculus I
- MATH 2215 Calculus II
- MATH 2220 Proof Writing
- MATH 3110 Foundations of Math Logic and Application
- MATH 3320 Set Theory
- MATH 3301 Discrete Mathematics
- MATH 3450 Real Analysis
- MATH 3460 Probability
- MATH 4210 Topology
- MATH 4301 Combinatorics and Graph Theory

**Research Interests:**

Mathematical Logic including Modal Logic; and Metamathematics.

For my publication on the semantics of third order modal logic, see

*Gödel’s Property Abstraction Operator and Possibilism*, Australasian Journal of Logic, managing editor Ed Mares, University of Wellington at Victoria, ISSN (electronic): 1448-5052 (11-2) 2014 Article no. 3

**Professional Interests:**

Recursion Theory; Model Theory including Saturated Model Theory; Set Theory including Metamathematics of Set Theory; Real Analysis and Topology; Measure Theory and Lebesque Integration; Non-standard Analysis; Abstract Algebra; Complex Analysis; Functional Analysis; Discrete Mathematics; Combinatorial Mathematics; Computational and Descriptive Complexity; Algorithms

**Personal Interests/Biography:**

I am very interested in mentoring talented and ambitious students in mathematical logic. At Hawaii Pacific University I have been able to have success teaching advanced theorems more typically taught in graduate school such as the Gödel’s First and Second Incompleteness Theorems and Tarski’s Theorem to interested undergraduate students. In my advanced logic class, students learn how to use the Compactness Theorem of First Order Logic to obtain a non-model of the reals that includes infinitesimals and perform non-standard analysis. Some of my students have been accepted to graduate programs at elite universities such as University of California at Berkeley and MIT. One of my students learned an entire year of advanced Model Theory culminating in a lecture on Direct Systems of Structures and Elimination of Quantifiers. In his second year, he studied the Independence of the Continuum Hypothesis with an introduction to Forcing. Another one of my students learned Advanced Recursion Theory including Turing Degrees.

I believe that mathematical logic can be very empowering to students and that the introduction of elegant proofs in logic to undergraduate students can be inspirational and transformational. To read more about the opportunities to study mathematical logic at Hawaii Pacific University, please see the listings for MATH 3110, 3320, and 4301 in our Course Catalog

**Associate Professor**

**Department Chair**

PH.D.

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