Math for Elementary Teachers
- Math 3131 Homeworks 1-13
- Lecture I –Course Introduction
- Lecture II -Numerals
- Lecture III –Relations
- Lecture IV –Functions
- Exercise on Functions
- Lecture V –Place Value
- Lecture VI –Subtraction
- Lecture VII –Multiplication
- A Multiplication Table
- Exercise on Multiplication Tables
- Lecture VIII –Division
- Lecture IX –Algorithms I
- Lecture X –A Division Algorithm
- Lecture XI –Estimation
- Lecture XII –Prealgebra
- Lectures XIII and XIV–Exponents
- Lecture XV –Factors and Prime Numbers
- Lecture XVII –Fractions
- Exercises on Factors and Primes
- Notes on the conversion of units
- Solving Algebra and Other Story Problems by Sybilla Beckmann
- Tree of Porphyry
Precalculus/Foundations of Mathematics
- On Definition (Definition according to Aristotle)
- On Truth
- On predicates and quantifiers
- On Sets
- On implication
- Truth tables
- A list of tautologies
- On validity
- A list of valid argument forms
- Order and inequality
- Properties of the real numbers
- Absolute value -summary and exercises
- Functions I
- Injective and surjective functions
- Functions II
- More on lines
- Graphing examples
- Image of a function
- Exercises on Functions
- Exercises on prime numbers and the greatest common factor
- Exponential functions–review
- Arithmetic sequences
- Geometric sequences
- Limits of sequences
- Polynomials – Lecture I
- Polynomials – Lecture II
- Complex Numbers – Lecture I
- Trigonometry -Lecture I
- Trigonometry -Review exercises
Calculus of Several Variables
Logic
Combinatorics
- Function Digraphs
- Notes on digraphs I
- Notes on digraphs II
- Digraph taxonomy
- Exercises on Dirichlet’s pigeon-hole principle
- Basic combinatorial results
Algebra
- Groups of small order
- Group axioms
- Elementary group properties
- Subgroups
- Group homomorphisms
- Isomorphisms
- Cyclic Groups
- Lagrange’s Theorem
US Citizenship Naturalization Test 2010 –with solutions
Old UPR Exams
All the exams are in pdf format. Inclusion of an exam in this list does not imply endorsement of its quality. Please visit the Mathematics Department Exam Page for more recent exams and reviews.
MATH 3001. Introductory Mathematics
MATH 3018. Precalculus and Analytic Geometry
- MATH 3018 933_1
- MATH 3018 932_2
- MATH 3018 933_3
- MATH 3018 933_4
- MATH 3018 991_1
- MATH 3018 991_2
- MATH 3018 991_3
- MATH 3018 991_4
MATH 3023. Precalculus I
- MATH 3023 992_4
- MATH 3023 992_3
- MATH 3023 992_2
- MATH 3023 992_1
- MATH 3023 991_4
- MATH 3023 991_3
- MATH 3023 991_2
- MATH 3023 991_1
- MATH 3023 992_4
- MATH 3023 992_3
- MATH 3023 992_2
- MATH 3023 001_3
MATH 3024. Precalculus II
- MATH 3024 981_1
- MATH 3024 981_4
- MATH 3024 982_1
- MATH 3024 982_2
- MATH 3024 982_3
- MATH 3024 982_4
- MATH 3024 991_4
- MATH 3024 992_1
- MATH 3024 992_2
- MATH 3024 992_3
- MATH 3024 992_4
- MATH 3024 041_1
- MATH 3024 042_1
- MATH 3024 042_2
- MATH 3024 042_3
- MATH 3024 042_4
- Notes on Trigonometry
MATH 3026. Statistics with Programming
MATH 3041. Introduction to Mathematics I
MATH 3151. Calculus I
- MATH 3151 992_1
- MATH 3151 992_2
- MATH 3151 992_3
- MATH 3151 992_4
- MATH 3151 993_1
- MATH 3151 993_2
- MATH 3151 993_3
- MATH 3151 993_4
- MATH 3151 993_5
- MATH 3151 993_6