The Nervous System Anatomy & Physiology

The Basics The nervous system is your body's decision and communication center. The central nervous system (CNS) is made of the brain and the spinal cord The peripheral nervous system (PNS) is made of nerves. Together they control every part of your daily life, from breathing and blinking to helping you memorize facts for a test. Brain Power: 55 sec. http://www.articlesbase.com/videos/5min/114222865

Neurons We’ll get back to these later….. A neuron is a nerve cell that is the basic building block of the nervous system. Neurons are specialized to transmit information throughout the body. They are responsible for communicating information in both chemical and electrical forms. There are also several different types of neurons responsible for different tasks in the human body. 1. Sensory neurons (afferent) carry information from the sensory receptor cells throughout the body to the brain. 2. Motor neurons (efferent) transmit information from the brain to the muscles of the body. 3. Interneurons are responsible for communicating information between different neurons in the body. We’ll get back to these later…..

Do Now! What are the two main parts of the nervous system? What “organs” are these two parts made up of? What is a neuron? What are the 3 different kinds of nerves?

Use the definitions below to correctly label this neuron axon - the long extension of a neuron that carries nerve impulses away from the body of the cell to other neurons. axon terminals - the hair-like ends of the axon cell body - the cell body of the neuron; it contains the nucleus (also called the soma) dendrites - the branching structure of a neuron that receives messages (attached to the cell body) myelin sheath - the fatty substance that surrounds and protects some nerve fibers node of Ranvier - one of the many gaps in the myelin sheath - this is where the action potential occurs during saltatory conduction along the axon nucleus - the organelle in the cell body of the neuron that contains the genetic material of the cell Schwann's cells - cells that produce myelin - they are located within the myelin sheath.

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Neurons Neuron Parts: • Soma: body of the cell • Dendrites: receive messages • Axon: sends messages Anatomy of a nerve http://www.youtube.com/watch?v=XgIaAs_ONG4&feature=related A Neurons has three main parts. The cell body, or soma, is a neuron's main cellular space. The soma houses the nucleus, in which the neuron's main genetic information can be found. The axon sends messages to other neurons. The dendrites receive messages from other neurons.

Two parts of Nervous system & Neuron video clip http://www.dnatube.com/video/2116/Anatomy-Nervous-System http://www.youtube.com/watch?v=DF04XPBj5uc&NR=1

How messages are sent and received Neurons send messages electrochemically. This means that chemicals cause an electrical signal. Chemicals in the body are "electrically-charged" -- when they have an electrical charge, they are called ions. The important ions in the nervous system are sodium and potassium (both have 1 positive charge, +), calcium (has 2 positive charges, ++) and chloride (has a negative charge, -). There are also some negatively charged protein molecules. It is also important to remember that nerve cells are surrounded by a membrane that allows some ions to pass through and blocks the passage of other ions. This type of membrane is called semi-permeable. Watch Bill Nye’s Greatest Science Discoveries on Neutrotransmitters.

How messages are sent and received continued Resting Membrane Potential : At rest, there is an excess of negative ions inside the neuron compared to the outside.

Membrane potential. . . Charge difference between the inside and outside of the membrane. The charge difference is due to the difference of concentrations of ions on either side of the cell membrane. Inside the membrane is negative and the outside is positive. This is due to the permeability of ions. There are more Na+ ions in the extracellular fluid and more K+ ions in the intracellular fluid. The membrane is more permeable to K+ which leaks out to the outside of the membrane giving it a positive charge. http://www.youtube.com/watch?v=iA-Gdkje6pg&feature=related

How messages are sent and received continued Action Potential When a point on the semi-permeable neural membrane is adequately stimulated by an incoming message, the membrane opens at that point, and positively charged ions flow in. This process is repeated along the length of the membrane, creating the neural impulse that travels down the axon, causing the neuron to fire. Electrical changes during the action potential. The incoming message must be above a certain threshold to cause a neuron to fire. After it fires, the neuron is returned to its resting state. This process happens very quickly, and within a few thousandths of a second the neuron is ready to fire again. http://www.teachertube.com/viewVideo.php?video_id=153535

An action potential is also called a nerve impulse. Action potential. . . A change in polarity across the membrane brought about by a stimulus. An action potential is also called a nerve impulse. In response to a stimulus the Na+ gates open. Na+ rushes into the cell. This causes the inside of the membrane to be positive and the outside to be negative. This reversal of charge is a depolarization. K+ gates open which allow K+ out of the cell: This causes a repolarization. This wave of depolarization followed by a wave of repolarization travels the length of a nerve axon and is called an action potential. It is also called a nerve impulse and it is how the nervous system communicates.

Refractory period. . . The period of rest before a neuron can be stimulated to fire off another action potential. The refractory period insures one way movement of action potentials along a nerve

Pygmies short, because growth hormone receptors are faulty and can’t interact with growth hormone

What causes this change in potential to occur? The stimulus causes the sodium gates (channel) to open and, because there's more sodium on the outside than the inside of the membrane, sodium then diffuses rapidly into the nerve cell. All these positively-charged sodium ions rushing in causes the membrane potential to become positive (the inside of the membrane is now positive relative to the outside). The sodium channels open only briefly, then close again. The potassium channels then open, and, because there is more potassium inside the membrane than outside, positively-charged potassium ions diffuse out. As these positive ions go out, the inside of the membrane once again becomes negative with respect to the outside.

A message passes from a sending neuron to a receiving neuron A message passes from a sending neuron to a receiving neuron. The neurotransmitters leave the sending neuron and enter the space between the sending and receiving neurons. This space is called the synapse. The neurotransmitters then hook up to a receptor on the receiving neuron to deliver their message. Once neurotransmitters have sent their message, they return and can be reabsorbed by the sending neuron in a process called reuptake. Reuptake allows the messengers to be reused. Two of these neurotransmitters are serotonin and norepinephrine. Low levels of serotonin and norepinephrine in the synapse are associated with depression and sadness. Some medications used to treat depression work by increasing the amount of certain neurotransmitters that are available to carry messages. Each type of antidepressant works on brain chemistry a little differently. All antidepressant medications influence how certain neurotransmitters, especially serotonin and norepinephrine, work in the brain. SSRIs and tricyclic antidepressants. Antidepressants, such as selective serotonin reuptake inhibitors, or SSRIs, and tricyclic antidepressants, work by slowing or blocking the sending neuron from taking back the released serotonin. In that way, more of this chemical is available in the synapse. The more of this neurotransmitter that is available, the more likely the message is received, and depression is reduced. To learn more about how these antidepressants work, see Tricyclic Antidepressants (TCAs) and Selective Serotonin Reuptake Inhibitors (SSRIs). MAOIs. The antidepressants known as MAO inhibitors, or MAOIs, affect neurotransmitters differently. Monoamine oxidase (MAO) is a natural enzyme that breaks down neurotransmitters. The drug MAOI disrupts the action of the enzyme MAO. In that way, there is an increase in the amount of neurotransmitters in the synapse, making more messengers available to the receiving neuron, and thus reducing depression. To learn more about how these antidepressants work, see Monoamine Oxidase Inhibitors (MAOIs).

Nerve Function and Drug Action: http://www.utexas.edu/research/asrec/neuroncartoon.html

Neuron parts http://garyfisk.com/anim/neuronparts.swf Animated visual: http://www.classzone.com/cz/books/bio_07/get_chapter_group.htm?cin=9&rg=animated_biology&at=animated_biology&var=animated_biology

Myelin and Nodes of Ranvier Axons are sheathed in a smooth fatty protein called myelin which insulates the axon, prevents the wrong ion channels from opening and considerably increases the speed that nerve impulses travel along the axon. Without the myelin, the axons would have to be about one hundred times their volume to achieve the same speed of nerve transmissions. The myelin is wrapped around the axon in many thin layers. The myelin does not enclose the axon in one entire sheath, but has gaps at intervals called the nodes of Ranvier. The precise function of these nodes is unknown but the nodes are major sites of sodium channels and may serve to prevent the decay of nerve impulses by effectively amplifying them. They may also act to anchor the myelin sheath to the axon and to isolate each segment of myelin from its neighbors. Work on rats with genetic deformities in their nodes of Ranvier has shown that these nodes are vital to efficient transmission of nerve impulses. How the myelin sheath works is discussed more fully in the section on myelin.

Quiz Time! Name the ….. 1. Part of the neuron that releases neurotransmitters into the synaptic cleft. 2. Fatty material that surrounds some axons. 3. Part that takes information away from the cell body. 4. The gaps in the myelin sheath. 5. Part of neuron that contains the nucleus. 6. Part that takes information to the cell body. 7. Organelle in neuron that contains genetic material. Answers are: 1. Axon terminal 4. Nodes of Ranvier 7. Nucleus 2. Myelin 5. Soma 3. Axon 6. Dendrites

The Central Nervous System Interesting Facts! The central nervous system is divided into two parts: the brain and the spinal cord. The average adult human brain weighs 1.3 to 1.4 kg (approximately 3 pounds). The brain contains about 100 billion nerve cells (neurons) and trillons of "support cells" called gila. The spinal cord is about 43 cm long in adult women and 45 cm long in adult men and weighs about 35-40 grams. The vertebral column, the collection of bones (back bone) that houses the spinal cord, is about 70 cm long. Therefore, the spinal cord is much shorter than the vertebral column. young frankenstein part 1

The CNS: The Brain

The cerebrum -- which is just Latin for "brain" -- is the newest (evolutionarily) and largest part of the brain as a whole.  It is here that things like perception, imagination, thought, judgment, and decision occur. The surface of the cerebrum -- the cerebral cortex -- is composed of six thin layers of neurons (nerve cells) and is referred to as the grey matter. It sits on top of a large collection of white matter pathways.  The cortex is heavily convoluted with “ridges” called gyri and “valleys” called sulci. If you were to spread the cortex out, it would actually take up about 2 1/2 square feet (2500 sq cm).  It includes about 10 billion neurons, with about 50 trillion synapses! The cerebral cortex is divided into four sections, called "lobes": the frontal lobe, parietal lobe, occipital lobe, and temporal lobe.

Grey vs. White Matter Grey matter – closely packed neuron cell bodies (making up the cerebral cortex) form the grey matter  of the brain. The grey matter includes regions of the brain involved in muscle control, sensory perceptions, such as seeing and hearing, memory, emotions and speech. White matter – neuronal tissue containing mainly long, myelinated axons, is known as white matter or the diencephalon. It makes up the cerebrum. The nuclei of the white matter are involved in the relay of sensory information from the rest of the body to the cerebral cortex, as well as in the regulation of autonomic (unconscious) functions such as body temperature, heart rate and blood pressure. Certain nuclei within the white matter are involved in the expression of emotions, the release of hormones from the pituitary gland, and in the regulation of food and water intake. These nuclei are generally considered part of the limbic system.

4 Main Parts of the Brain

The Brain The cerebral cortex is comprised of the: frontal lobe, parietal lobe, occipital lobe, and temporal lobe.

What do each of these lobes do? Frontal Lobe- associated with reasoning, planning, parts of speech, movement, emotions, and problem solving

Functions associated with the frontal lobes: Conscious thought Concentration Perseverance Judgment Attention span Impulse control - self monitoring and supervision Problem solving Organization Critical thinking Forward thinking Ability to feel and express emotions Empathy YouTube - NEURONS AND NEURO-TRANSMITTERS

What do each of these lobes do? Frontal Lobe- associated with reasoning, planning, parts of speech, movement, emotions, and problem solving Parietal Lobe- associated with movement, orientation, recognition, perception of stimuli

Parietal Lobe The parietal lobes can be divided into two functional regions. One involves sensation and perception and the other is concerned with integrating sensory input, primarily with the visual system.

What do each of these lobes do? Frontal Lobe- associated with reasoning, planning, parts of speech, movement, emotions, and problem solving Parietal Lobe- associated with movement, orientation, recognition, perception of stimuli Occipital Lobe- associated with visual processing

Occipital lobes The OC are the center of our visual perception system. They are not particularly vulnerable to injury because of their location at the back of the brain, although any significant trauma to the brain could produce subtle changes to our visual-perceptual system, such as visual field defects.

What do each of these lobes do? Frontal Lobe- associated with reasoning, planning, parts of speech, movement, emotions, and problem solving Parietal Lobe- associated with movement, orientation, recognition, perception of stimuli Occipital Lobe- associated with visual processing Temporal Lobe- associated with perception and recognition of auditory stimuli, memory, and speech

The dominant side is usually the left hand side and governs- TEMPORAL LOBES: Located at sides of head above ears, the temporal lobes form the wings of the soul of our living caduceus. Functions: The dominant side is usually the left hand side and governs- Hearing ability Understanding and processing language Memory acquisition - particularly long term memory Some visual perceptions Categorization of objects. The no dominant side or right side governs- Recognition of facial expressions Decoding vocal intonation Rhythm Music Visual learning How your memory works?

A deep furrow divides the cerebrum into two halves, known as the left and right hemispheres. Sometimes the right hemisphere is associated with creativity and the left hemispheres is associated with logic abilities. The corpus callosum is a bundle of axons which connects these two hemispheres. The right hemisphere controls the left side of the body, and the left hemisphere controls the right side.

Do Now! What are the 4 parts of the cerebrum? The convolutions of the cerebrum are comprised of ridges and valleys. What are the ridges called? The valleys? What part of the brain is dedicated to visual perceptions? What part of the brain is associated with reasoning, planning, parts of speech, movement, emotions, and problem solving? 5. What part of the brain is associated with movement, orientation, recognition, perception of stimuli? 6. What part of the brain is associated with perception and recognition of auditory stimuli, memory, and speech? 7. What is the deep furrow that divides the cerebrum into two halves known as?

The Cerebellum The cerebellum, or "little brain", is similar to the cerebrum in that it has two hemispheres and has a highly folded surface or cortex.

Coordination of voluntary movement posture Balance and equilibrium CEREBELLUM: Located at the base of the skull, and attached to the rear of the brain stem. Functions: Coordination of voluntary movement posture Balance and equilibrium Some memory for reflex motor acts.

Limbic System: The limbic system, often referred to as the "emotional brain", is found buried within the cerebrum. Like the cerebellum, evolutionarily the structure is rather old. This system contains the: thalamus (almost all sensory information enters this structure where neurons send that information to the overlying cortex ), hypothalamus (functions including homeostasis, emotion, thirst, hunger, circadian rhythms, and control of the autonomic nervous system. In addition, it controls the pituitary ) amygdala (memory, emotion, and fear ), hippocampus (important for learning and memory, for converting short term memory to more permanent memory, and for recalling spatial relationships in the world about us) Sense of smell

BRAIN STEM: Located deep in the brain, leads to spinal cord BRAIN STEM: Located deep in the brain, leads to spinal cord. Often referred to as The 'Reptilian' or 'Primitive' Brain. The majority of the cranial nerves exit from the brain stem at the pons. The midbrain is the smallest region of the brain that acts as a sort of relay station for auditory and visual information. The pons connects the medulla to the cerebellum and helps coordinate movement on each side of the body. The medulla is located directly above the spinal cord and controls many vital autonomic functions such as heart rate, breathing and blood pressure.

Brain stem: 3 parts Lower animals have only a medulla. The brain stem controls the reflexes and automatic functions (heart rate, blood pressure), limb movements and visceral functions (digestion, urination).

Edheads.org Virtual brain surgery

Fissure: any cleft or groove, normal or otherwise, especially a deep fold in the cerebral cortex involving its entire thickness.

Sheep Brain Dissection Guide http://www.wellesley.edu/Biology/Concepts/Html/sheepbrain.html http://academic.scranton.edu/department/psych/sheep/

Dura mater Superior ID

After splitting the cerebral hemispheres Part 1: Sheep brain dissection http://www.youtube.com/watch?v=y7gEWzPqm94

Ventral side of the brain Part 2: Brain dissection http://www.youtube.com/watch?v=jr3qSaUzc6Q

Here's the cerebellum pushed downward to expose the superior and inferior colliculi and pineal gland The Superior colliculus (2 parts) and the inferior colliculus (2 parts) make up the corpora quadrigemina are the reflex centers involving hearing and vision.

The Nerves The largest nerve in the body is the sciatic and it splits into the common tibial and fibular nerves that run down each leg.

How the messages travel

PNS As part of the Peripheral Nervous System, nerves reach from your brain to your face, ears, eyes, nose, and spinal cord... and from the spinal cord to the rest of your body. 1) Motor neurons (motoneurons) carry signals from the central nervous system to the outer parts (muscles, skin, glands) of your body. 2) Sensory neurons carry signals from the outer parts of your body (periphery) into the central nervous system. 3) Receptors sense the environment (chemicals, light, sound, touch) and encode this information into electrochemical messages that are transmitted by sensory neurons. 4) Interneurons connect various neurons within the brain and spinal cord.

What’s a Reflex? You need to detect a change in the environment (a stimulus) and react to the change (a response) in a way that maintains homeostasis. When you do this without thinking, it is called a reflex.

Reflex Pathways The simplest type of neural pathway is a monosynaptic (single connection) reflex pathway, like the knee-jerk reflex. 1. When the doctor taps the right spot on your knee with a rubber hammer, receptors send a signal into the spinal cord through a sensory neuron. 2. The sensory neuron passes the message to a motor neuron that controls your leg muscles. Nerve impulses travel down the motor neuron and stimulate the appropriate leg muscle to contract. 3. The response is a muscular jerk that happens quickly and does not involve your brain. Humans have lots of hard-wired reflexes like this, but as tasks become more complex, the pathway "circuitry" gets more complicated and the brain gets involved.

Revisiting the Knee-Jerk Response What is the stimulus? The hammer hits the tendon. What is the response? The muscle contracts, causing the foot to jerk upward.

How is the Hammer Tap Detected? The muscles in your leg have stretch receptors. They react to a change in length of the muscle. When the hammer hits the tendon at the knee, it makes a muscle in the front of your thigh longer (stretches it). That stimulates the stretch receptors in that muscle.

Other Reflexes: Stimulus Response An insect flying towards your eye Blinking The aroma of your favorite food Salivation A bright light shining in your eye Pupils get smaller A nasty odor Nausea What detects the stimulus in each case? Receptor Cells

The Response When the receptor is stimulated, it sends a message to a part of your body that effects the correct response. This is called the effector.

Reflex arc http://www.classzone.com/cz/books/bio_07/get_chapter_group.htm?cin=9&rg=animated_biology&at=animated_biology&var=animated_biology

How the Message Travels From the Receptor to the Effector. A sensory neuron carries the message from the receptor to the central nervous system (the spinal cord and brain). A motor neuron carries the message from the central nervous system to the effector. This is a reflex arc.

Motor (efferent) Neurons Is divided into two groups: 1. Autonomic system The ANS In most situations, we are unaware of the workings of the ANS because it functions in an involuntary, reflexive manner. 2. Somatic system (back to this in a moment)

Name the Neurons Neuron 2 ? Sensory Neuron

Name the Neurons Neuron 3 ? Interneuron

Name the Neurons Neuron 4 ? Motor Neuron

The ANS is most important in two situations: In emergencies that cause stress and require us to "fight" or take "flight" (run away)                       In non-emergencies that allow us to "rest" & "digest."           . The ANS is divided into three parts: 1. The sympathetic nervous system 2. The parasympathetic nervous system 3. The enteric nervous system (is a meshwork of nerve fibers that innervate the viscera (gastrointestinal tract, pancreas, and gall bladder).

ANS Parasympathetic Sympathetic: This calls for "Rest and Digest" responses. Now is the time for the parasympathetic nervous to work to save energy - your blood pressure decreases, your heart beats slower, and digestion can start. Sympathetic: These are "Fight or Flight" responses. In these types of situations, your sympathetic nervous system is called into action - it uses energy - your blood pressure increases, your heart beats faster, and digestion slows down.

The Autonomic Nervous System Structure Sympathetic Stimulation Parasympathetic Stimulation Iris (eye muscle) Pupil dilation Pupil constriction Salivary Glands Saliva production reduced Saliva production increased Oral/Nasal Mucosa Mucus production reduced Mucus production increased Heart Heart rate and force increased Heart rate and force decreased Lung Bronchial muscle relaxed Bronchial muscle contracted Stomach Peristalsis reduced Gastric juice secreted; motility increased Small Intestine Motility reduced Digestion increased Large Intestine Secretions and motility increased Liver Increased conversion of glycogen to glucose Kidney Decreased urine secretion Increased urine secretion Adrenal medulla Norepinephrine and epinephrine secreted Bladder Wall relaxed Sphincter closed Wall contracted Sphincter relaxed

Back to The Somatic Nervous System The somatic nervous system consists of peripheral nerve fibers that send sensory information to the central nervous system AND motor nerve fibers that project to skeletal muscle. The picture shows the somatic motor system. The cell body is located in either the brain or spinal cord and projects directly to a skeletal muscle.

This very strange creature in the Glasgow Science Centre is the Homunculus. The different parts of the body are sized according to the amount of nerves present in that part of the body.

Disorders of the Nervous System

Alzheimer’s disease: progressive degenerative brain disease that results in dementia associated with a shortage of acetylcholine (an important neurotransmitter) and structural changes in brain areas involving cognition and memory. Because nerve cells do not undergo mitosis, new cells can not be generated.

Aluminum and Alzheimer’s

Cerebrovascular accident (CVA): brain dysfunction where blood supply to a region is blocked and vital brain tissues dies as by a blood clot or ruptured blood vessel. This is more commonly called a stroke.

Cerebral Edema a condition characterized by the presence of a large amount of water in the brain. If not treated, it can be fatal, or cause severe brain damage, and the quicker a patient is treated, the better his or her chances of recovery will be. Because this condition can be extremely serious, evaluations to check for signs of cerebral edema are common when patients are brought in for head trauma, because doctors want to catch it as early as possible.

Multiple sclerosis: when the myelin sheath around the axon deteriorates the electrical current is short circuited. The person may experience visual and speech disturbances and also lose muscle control.

M.S.

MS In multiple sclerosis, the myelin sheath is stripped off from the neuron which considerably reduces the speed of conduction of nerve transmissions. This process is known as demyelination. The effects of this is to considerably slow down the speed of nerve transmissions along the demyelinated axons. The myelin is often laid down again in a repair process known as remyelination which can often restore near normal functioning to the axon. However, and particularly in progressive stages of the disease, the myelin can be replaced with scar tissue or the axonal body itself can be damaged.

Famous People with MS Annette Funicello – singer, dancer, former Mouseketeer Clive Burr - Iron Maiden Drummer Alan Osmond

Danny Wallace – Soccer Player

New Treatment: Bee venom helps MS http://www.youtube.com/watch?v=7mbBIZHZ-yY

Wrist drop: The inability to extend the hand at the wrist because the radial nerve has been damaged.

Cerebral Edema The brain reacts to severe head trauma by retaining water. As a result, the brain swells. The pressure grows as the brain presses on the skull. This can be fatal or result in severe brain damage.

Siatic nerve Wrist drop: inability to extend the hand at the wrist because the radial nerve has been damaged. Cerebral edema: The brain reacts to severe head trauma by retaining water. As a result, the brain swells. The pressure grows as the brain presses on the skull. This can be fatal or result in brain damage. Alzheimer’s disease: progressive degenerative brain disease that results in dementia associated with a shortage of acetylcholine (an important neurotransmitter) and structural changes in brain areas involving cognition and memory. Because nerve cells do not undergo mitosis, new cells can not be generated. Cerebrovascular accident (CVA): brain dysfunction where blood supply to a region is blocked and vital brain tissues dies as by a blood clot or ruptured blood vessel. This is more commonly called a stroke. Multiple sclerosis: when the myelin sheath around the axon deteriorates the electrical current is short circuited. The person may experience visual and speech disturbances and also lose muscle control. FYI: The largest nerve in the body is the ___________________ and it splits into the common tibial and fibular nerves that run down each leg. Siatic nerve

The End Complete your study guide to prepare for the test. The test has…. 29 multiple choice (2 pts each) 6 labeling neuron (2 points each) 10 fill in the blanks (2 pts each) 6 label parts of the brain 100 points

Info on chemical on the nerves: Nervous System Info on chemical on the nerves: http://faculty.washington.edu/chudler/weap.html

Chemical Weapons: Nerve Agents You may have read newspaper or magazine articles about the possible use of chemicals during a war or a terrorist attack. Many of these chemicals affect the nervous system and are therefore called nerve agents. Nerve agents are similar to insecticides and they can be deadly if people are exposed to them. Unfortunately, this has already happened. On March 20, 1995, twelve people were killed and over 5,000 were injured when a nerve gas called "sarin" was released in the Tokyo subway system. People may have also been exposed to nerve agents during the conflict ("Gulf War") in the Middle East. It is possible that many countries have access to these dangerous weapons and future human exposure to these chemicals is possible. Breathing a lethal dose of these chemical can kill in 15 minutes; a lethal dose on the skin (not much more than a single grain of rice!!) can kill in only 1-2 minutes!! To get an idea of how deadly these chemicals are, do the math.