# Bachelor of Arts Core

**CogNatE Natural Philosophy Academy **incorporates **Classical Christian Education** into its program. **The Trivium** and The **Quadrivium** are the foundations of the **Associate of Arts in Natural PhiloSophae**. The **Bachelor of Arts in Natural PhiloSophae **continues with three available cognates: **Natural PhiloSophae**, **BioLogica** (Biology and Chemistry), or **MatheMatica** (Mathematics and Physics). The core consists of ** ApoLogia**,

**,**

*PreCalculus***,**

*Statistics***,**

*Paideia***, and**

*Modeling***Research/Thesis**. Each of the

**Cognates**completes 60+ credit hours for the degree.

ApoLogia I, II | PreCalculus | Modeling |

Paideia | Statistics | Research/Thesis |

Chemistry I, II | General BioLogica I, II | Physics with Algebra I, II |

AstroNomia with Relativity | GeoGraphica | CrystalloGraphica |

Chemistry I, II | Physics with Algebra I, II | Cellular BioLogica |

Molecular: Organic | Molecular: Biochemistry | CrystalloGraphica |

Systems BioLogica | GenOmica |

MatheMatica Proof | Calculus I, II, III |

Probability or Number Theory | AstroNomia with Relativity |

Real Analysis or Algebraic Structures | Physics with Calculus I, II |

All courses through the **CogNatE Natural Philosophy Academy** share program distinctives:

- Courses apply grammar, dialectics, and rhetoric to integrate the topic with God’s revelation through His creation and Moral PhiloSophae and OrthoDoxia, emphasizing the inseparability of all.
- Courses emphasize character development, ethics, and virtue as these intersect with the subject matter and promote adopting, adhering to, and promoting a scriptural paideia.
- Courses connect topical investigations to real-world situations, demonstrating that academic topics are interconnected with the world, reminding us of God’s sovereignty in creation, and assisting in navigating our God-given lives.
- Lessons open and close with prayer and Scripture, employ the Socratic Method (inquiry-based instruction), and emphasize logic, reasoning, and critical thinking.

**BIOL 2003 General BioLogica I: **Explores the internal design and organization of eukaryotic cellular and subcellular structures and considers the structure and function relationships that govern cellular processes at the molecular level. Surveys organelle and membrane function, cell-cell signaling, cell movement, cell adhesion, the extracellular matrix, Energy and Metabolism, Respiration, and Photosynthesis. This course includes a lab.

**BIOL 2023 General BioLogica II: **Considers the design and organization of representative organisms of Prokaryotic: Archaea and Bacteria and Eukaryotic: Plants, Fungi, Protists, and Animals; and investigates the diversity of structure and physiology of organisms and their interactions within ecosystems and the biome. This course includes a lab.

**BIOL 3003: Cellular BioLogica: **Investigates the internal design and organization of eukaryotic cellular and subcellular structures, paying attention to the structure and function relationships that govern cellular processes at the molecular level. Surveys organelle and membrane function, cell-cell signaling, cell movement, cell adhesion, the extracellular matrix, Energy and Metabolism, Respiration, and Photosynthesis. This course includes a lab.

**BIOL 3023 Systems BioLogica: **Explores the design and organization of representative organisms of Prokaryotic: Archaea and Bacteria and Eukaryotic: Plants, Fungi, Protists, and Animals; and investigates the diversity of structure and physiology of organisms and their interactions within ecosystems and the biome. This course includes a lab.

**BIOL 3043 Genomics BioLogica: **Considers genes, genetic variation, and heredity in organisms and investigates the Genomics of DNA as the molecular basis of heredity. Concentration is placed on the processes of Replication (creating identical DNA strands), Transcription (converting DNA code into messenger mRNA), and translation, which decodes mRNA into amino acids, forming proteins essential for life. This course inclides a lab.

**BIOL 5003 BioLogica Paideia I: **Addresses how the practice of BioLogica topics and investigations are inextricably connected with implementing this paideia in our lives and connecting these BioLogica topics with Moral PhiloSophae and OrthoDoxia.

**BIOL 5023 BioLogica Modeling I: **Investigates the generation of physical, conceptual, or BioLogica representations of natural phenomena that are difficult to observe directly. Models are used to explain and predict the behavior of real objects or systems and are used in Natural PhiloSophae disciplines.

**BIOL 5043 BioLogica Research/Thesis I: **Dives into some historical and current BioLogica research findings and how they affect our world and lives. Each ach student will select a BioLogica topic that meaningfully connects to the student’s life or world, argue for its interconnected importance, complete a research project on that topic with the instructor’s guidance, and collaborate with some classmates on a larger group research project.

**CHEM 2003 BioLogica Chemistry I: **Considers matter’s composition, structure, and properties, including the electronic structure of atoms, periodic trends, ionic and molecular bonding, and intermolecular forces. This course includes a lab.

**CHEM 2023 BioLogica Chemistry II: **Investigates: Quantitative principles in chemistry including dimensional analysis, stoichiometry, chemical equations, redox reactions, oxidation numbers, balancing equations, limiting reactants, percent yield, and empirical formulas; Principles of thermochemistry including enthalpy, calorimetry, heat of formation, and Hess’s law; Gas Laws, including Boyle’s law, Charles’s law, and Avogadro’s law; Solutions including concentrations, colligative properties, and solubility; Equilibrium including Le Chatelier’s principle, constants, and reaction rates. Acid-base reactions including pH calculations, and titrations; and Nuclear chemistry including nuclear reactions, radioactive decay, and applications of nuclear energy. This course includes a lab.

**CHEM 2043 Crystallo Graphica: **Explores Euclid’s Book XIII, delving into the construction of the five regular Platonic solids, and examining Euler’s formula and the study of crystals. Crystallography highlights the significance of crystal structures in describing organized layouts and enabling applications in X-ray, neutron, and electron diffraction. Investigates crystallographic databases, emphasizing identification alignment with the International Union of Crystallography. Explores crystal structures, including minerals, metals-alloys, and biological macromolecules, are explored, with foci on metals-alloys and intermetallics. This course includes a lab.

**CHEM 3003 BioLogica Molecular: Organic: **Considers the organic chemistry study of CHNOPS and Halogen compounds’ structure, properties, and reactions in covalent bonding. Emphasizes the chemical composition, formula, and functional group structures of Oxygen, Nitrogen, and Sulfur. Demonstrates the physical and chemical properties and chemical reactivity for synthesizing natural products, drugs, polymers, and organic molecules. This course includes a lab.

**CHEM 3023 BioLogica Molecular: Biochemistry: **Investigates the structures and functions of organisms, tissues, and cells at the molecular level and emphasizes the study of biomolecules, such as nucleic acids, lipids, proteins, and carbohydrates, and their significance in cellular processes. Covers topics related to cell signaling, hormones, and the Krebs cycle. Explores different levels of protein structure, enzymes, their catalytic properties, and the factors that influence enzyme activity. Examines various cellular processes, including cell signaling and the role of hormones in coordinating physiological responses. This course includes a lab.

**CHEM 5003 Chemistry Paideia I: **Considers how the practice of Chemistry topics and investigations are inextricably connected with implementing this paideia in our lives and connecting these Chemistry topics with Moral PhiloSophae and OrthoDoxia.

**CHEM 5023 Chemistry Modeling I: **Investigates the generation of physical, conceptual, or Chemistry representations of a natural phenomenon that are difficult to observe directly. Models are used to explain and predict the behavior of real objects or systems and are used in Natural PhiloSophae disciplines.

**CHEM 5043: Chemistry Research/Thesis I: **Considers historical and current Chemistry research findings and how they affect our world and lives. Students will select a Chemistry topic that meaningfully connects to the student’s life or world, argue for its interconnected importance, complete a research project on that topic with the instructor’s guidance, and collaborate with some classmates on a larger group research project.

**MATH 2003 Statistics: **Introduces statistical problem solving and methodology. Includes representations of univariate and bivariate data; designed methods for data collection and the role of randomness in statistical studies; probability, statistical distributions, confidence intervals, and hypothesis testing; statistical estimation and significance. Emphasizes conceptual understanding and interpretation of results rather than theoretical development.

**MATH 2023 PreCalculus: **Considers: functions (trigonometric, power, polynomial, rational, exponential, logarithmic, logistic, and polar) and transformations; trigonometry (unit circle; trigonometric functions, equations, and graphs; right triangle trigonometry; trigonometric functions and inverses; laws of sines and cosines; trigonometric identities; double and half-angle formulas); Fundamental Theorem of Algebra; conic sections; vectors; complex numbers in trigonometric form; polar equations of conic sections; 3-D coordinate system; The Binomial Theorem; matrix algebra; sequences and series; and limits.

**MATH 2043 Mathe Matica Proof: **Investigates methods of mathematical proof including propositional calculus, predicate calculus, and several first-order theories. Informal proof topics are drawn from number theory, set theory, and other areas of mathematics.

**MATH 3003 Calculus I: **Investigates limits, continuity, differentiation, applications of the derivative, the differential, the definite integral, the fundamental theorem, and applications of the definite integral.

**MATH 3023 Calculus II: **Considers logarithmic and exponential functions, circular functions and their inverses, techniques of integration, improper integrals, infinite series, Taylor polynomials, and power series.

**MATH 3043 Calculus III: **Investigates parametric equations, vectors, vector-valued functions, functions of several variables, double and triple integrals, and vector analysis.

**MATH 4003 Real Analysis: **Explores the treatment of the calculus of functions of real variables, including sequences, limits of functions, continuity, and differentiation.

**MATH 4023 Algebraic Structures:** Considers equivalence relations, groups, subgroups, homomorphisms, isomorphisms, and a survey of other algebraic structures such as rings, integral domains, and fields.

**MATH 4043 Probability: **Introduces discrete probabilities and related applications leading to problem solving from the fundamentals of probability. Topics include general probability, random variables for univariate and multivariate distributions, independence, conditional probability, continuous and discrete distributions, and various named distributions, including the normal distribution, moments from univariate and multivariate distributions, and probability and moment-generating functions.

**MATH 4063 Number Theory: **Investigates elementary number theory including: primes, congruences, quadratic reciprocity, Diophantine equations, irrational numbers, continued fractions, partitions, the Euclidean Algorithm, Fibonacci numbers, the golden ratio, modular arithmetic, Fermat’s Little Theorem, RSA public key cryptography, Gaussian integers, and others.

**MATH 5003 Mathe Matica Paideia I: **Considers how the practice of MatheMatica topics and investigations are inextricably connected with implementing this paideia in our lives and connecting these MatheMatica topics with Moral PhiloSophae and OrthoDoxia.

**MATH 5023 Mathe Matica Modeling I: **Investigate the generation of physical, conceptual, or MatheMatica representations of natural phenomena that are difficult to observe directly. Models are used to explain and predict the behavior of natural objects or systems and are used in MatheMatica disciplines.

**MATH 5043 Mathe Matica Research/Thesis I: **Students will select a MatheMatica topic that connects to the student’s life or world, argue for its interconnected importance, complete a research project on that topic with the instructor’s guidance, and collaborate with some classmates on a larger group research project.

**NPHI 2043 GeoGraphica: **Introduces the basic concepts of Physiography and Geomorphology, tectonic activity, surficial earth movements, weathering, erosion, and deposition caused by wind, glacial ice, and streams. Investigates Geographical Information Systems (GIS), digitizing maps and spatial data, storage and retrieval, analysis, and producing maps, tables, and remote sensing processes. This course includes a lab.

**NPHI 5003 Natural PhiloSophae Paideia I: **Considers how the practice of Natural PhiloSophae topics and investigations are inextricably connected with implementing this paideia in our lives and connecting these Natural PhiloSophae topics with moral PhiloSophae and OrthoDoxia.

**NPHI 5023 Natural PhiloSophae Modeling I: **Investigate the generation of physical, conceptual, or Natural PhiloSophae representations of a real phenomenon that are difficult to observe directly. Models are used to explain and predict the behavior of real objects or systems and are used in Natural PhiloSophae disciplines.

**NPHI 5043 Natural PhiloSophae Research/Thesis I: **Student will select a Natural PhiloSophae topic that meaningfully connects to the student’s life or world, argue for its interconnected importance, complete a research project on that topic with the instructor’s guidance, and collaborate with some classmates on a larger group research project.

**PHYS 2023 Physics with Algebra I: **Considers Classical Physics built upon Algebra and the foundational principles of Newtonian mechanics, work, energy, power, mechanical waves, sound, friction, free-body diagrams, and gravitational forces. This course includes a lab.

**PHYS 2043 Physics with Algebra II: **Investigates Classical Physics built upon Algebra and the foundational principles of simple circuits, charge distribution, conduction, induction, electric forces, and electromagnetic forces are investigated. This course includes a lab.

**PHYS 3003 AstroNomia with Relativity: **Explores astronomy, the revolutionary concepts of Einstein’s theory of gravitation, and the principles of Special and General Relativity, including the nature of space-time, the concept of gravitational waves, and the impact of massive objects on the curvature of space. Investigates the mathematical frameworks that underpin these theories, equipping students with the tools necessary to analyze and solve problems related to relativity. This course includes a lab.

**PHYS 3023 Physics with Calculus I: **Considers Classical Physics built upon Calculus and the foundational principles of Newtonian mechanics, work, energy, power, mechanical waves, sound, friction, free-body diagrams, and gravitational forces are investigated. This course includes a lab.

**PHYS 3043 Physics with Calculus II: **Investigates Classical Physics built upon Calculus and the foundational principles of simple circuits, charge distribution, conduction, induction, electric forces, and electromagnetic forces are investigated. This course includes a lab.

**PHYS 5003 Physics Paideia I: **Explores how the practice of Physics topics and investigations are inextricably connected with implementing this paideia in our lives and connecting these Physics topics with Moral PhiloSophae and OrthoDoxia.

**PHYS 5023 Physics Modeling I: **Investigate the generation of physical, conceptual, or Physics representations of a natural phenomenon that are difficult to observe directly. Models are used to explain and predict the behavior of real objects or systems and are used in Natural PhiloSophae disciplines.

**PHYS 5043 Physics Research/Thesis I:** Students will select a Physics topic that meaningfully connects to the student’s life or world, argue for its interconnected importance, complete a research project on that topic with the instructor’s guidance, and collaborate with some classmates on a larger group research project.

**THEO 3023 ApoLogia I:** Grapples with foundational questions of knowledge and belief from a Classical Christian perspective through careful analysis of primary texts, philosophical frameworks, and historical contexts. Explores how influential thinkers have contributed to the ongoing conversation about the intersection of faith and reason in Christian epistemology.

**THEO 3043 ApoLogia II: **Explores the rich tapestry of Classical Christian Apologetics and the tools to engage thoughtfully with the intellectual foundations that underlie the defense of Christian belief. Examining primary texts, theological reflections, and practica